This situation has a bit of an odd background and the whole thing is LONG--TLDR at the bottom. On mobile, formatting, etc.

For clarity purposes and because it's how stories go, I'll begin at the beginning. Last summer, my husband (37M) and I(30F) saw a naked woman through our front window. She was walking down the street looking lost. It was hot enough that the pavement had to have been burning her feet. I'm a nurse by trade and I try to be a helper, so I grabbed a robe and ran out to collect her. She was confused, but compliant and came with me with no issues. My two children were under 2 at the time and in the house with my husband, and because I didn't know what was going on with her I brought her to my back porch. I got her some water and called 911. A police officer came, and from what he said I gathered that this was not an isolated incident. He called an ambulance, and I then learned that this woman, Laura, lives a few blocks away and has epilepsy as well as some other mental and physical health issues. She offered my robe back, I told her to keep it and take care of herself, she's carted off to the hospital and I figured that was that.

A few weeks later, she comes knocking on my front door. She asked if it was me who found her, hugged me, and gave me a card that was filled with Bible verses. I'm not religious in the slightest(important later), but we live in a small, religious town and I usually just take these types of sentiments as a good-faith effort at connection and play/nod along. We re-introduced ourselves and chatted for a moment, and she told me she got my address from the police station. She seemed harmless enough, and I figured with town being as small as it is she would have found me eventually anyway, so it didn't bother me at the time. Again, I figured that was that.

No, no, no. My husband and I are big walkers. If it's nice out, we have the kids out and about in the stroller or running on the sidewalk. Laura is also a big walker out of necessity--she can't drive because of her epilepsy. She's also very lonely and likes to chat with people around town. We would stop and talk when we ran into each other, she'd coo over the kids and ask if she could give them candy. I'd tell her no, they're too little. She'd seem a tiny bit offended, but it was never a problem.

Cut forward to Christmas time. We had family visiting from overseas, and who shows up at the door but Laura. We tell her we have family visiting right now and she says, "Oh great!" And just....walks inside. I figured just relying on social norms would cause her to come in, say happy holidays, good to see ya and go on her way. I didn't know how to handle it in the moment, so we all just rolled with it. Nobody wanted to hurt her feelings and we know that she has no family around. She stayed for about an hour, showed endless pictures of her kids and grandkids who all live out of state, showed us their dogs, asked everyone in the room about the Lord, testified for a few minutes and then left after a gentle Midwestern nudge from my husband.

Since then, the visits have been getting more and more frequent. They started off about 3 weeks apart, then 2, then weekly, and now it's a few times a week. These visits happen at all times of day--mid-morning, nap time, dinner time, AFTER dinner time(i.e. bath and bedtime), which really threw me off. She brings the kids things they don't need, which whatever, grandma stuff. But then she's started questioning us about our relationship with the Lord more frequently. We try to either dodge these questions or shut them down gently. As I said, I'm not religious. My huband isn't either, and we're raising our kids in a way that they'll hopefully choose whatever feels right to them when the time comes. Regardless, I'm not trying to change her mind on her religion and I don't want her trying to argue with me about it, especially in my own house. I digress.

My kids are still 2 and under, so naps are VERY important in my house. She'll come to the door and knock incessantly(sometimes for minutes straight) until I answer. The 2nd or 3rd time she did this, after about 30 seconds of knocking, she TRIED THE DOORKNOB. Thank god it was locked, but I was sitting with my 2 napping babies on my lap just shaking until she finally fucked off. Needless to say, she cut a couple naps way too short and then threw off the whole house for a couple days(if you have or have ever had young children, you understand). I got fed up and started putting a sign on the door at naptime that says "Naptime Please Don't Knock." This worked for a couple weeks. She'd comment on it the next time we saw her, "I was gonna come visit but mommy put a sign on the door," etc. She talks to me through my 2-year-old most of the time. I've started acting like I don't hear her unless she speaks to me directly.

Now to this week. She's ignoring my nap sign and knocking anyway. I ignored her and she went on her way, then came back a few hours later and knocked again(sign was down at this point). I let her in against my better judgment, and she just keeps getting more(too) comfortable with my children. She tried to kiss them both and I had to tell her no. I eventually get her to leave. 2 days ago, I had both kids with me at a friend's house. My husband got home in that window and called me saying, "Laura's here wondering when you'll be home. She has gifts for the kids. She says she wants to see their faces when they open them" At this point, having her around makes me extremely uncomfortable and I'm actively formulating my rid-ourselves-of-Laura plan. We didn't go home until bedtime. My husband later told me that he tried just telling her to leave the gifts and that he didn't know when I'd be home, but she kept repeating herself, wouldn't leave, and then said, "You have a phone, don't you? You can call her." He's a nice man, he doesn't want to hurt her either, so he did it. He also told me that in this conversation, he learned that she doesn't remember what gifts she gives to the kids. We've had suspicions before because she'll tell us the same story or show us the same pictures almost every time we see her, but I'm getting progressively less comfortable with this person who clearly has several screws loose or missing being around my family and in my home.

Then yesterday. I knew she'd be coming around because she's persistent like that. My husband was gone all day. I was jumpy. My sister was here with me, which I'm endlessly thankful for. Knock, Knock, Knock, here's Laura. Okay. We let her in, I'm telling myself it'll be fine, I'm overreacting and just need to try to find some hospitable warmth in my cold, millennial heart. She gives them the bag. It's a Kroger bag, I'm convinced she just finds random stuff and brings it over. It's fine, we like thrifted/found stuff. There's a sucker in the bag. She asks if my oldest can have it. I said, "I'll just put that up for later," with every intention of tossing it. She insists on making sure he sees it first, so of course he throws a tantrum. He's 2, you can't show him candy, take it away, and then expect him to be fine. But I'm not giving him the damn sucker, so tantrum it was. She moved to pick him up. I said no, I got him, and went to grab him. She insisted, "I got him, I got him!" I yelled, "LAURA!" wrestled him away, and took him to the other room. I should have told her it was time to go at that point. I don't know why I didn't. It seemed like this interaction didn't even raise her pulse or register in her mind as wrong. She stuck around for another 10 minutes. She told me my kids remind her of her grandkids. That they're so cute. That she saw them and just fell in love. I was still shaking from having to wrestle my son out of her arms moments before. I manufactured an excuse to get her out the door.

I called the non-emergency line just to see if they could tell me anything about her. Come to find out, this isn't uncommon for her. She latches on to families with young kids, has no social awareness or respect for boundaries. The officer I talked to said, "She's a sweet woman, and she's been harmless up to this point. She's usually reasonable when she's taking proper care of herself, but you never know with her condition. You'll just have to be very firm and direct and tell her you're uncomfortable." Fair.

My issue is--how in the world do I approach this? There's no doubt in my mind that she'll come knocking again. We'll see her around town. I need to tell her that she's not welcome in my house. She's not. She crossed a huge line trying to keep my kid in her arms. I'm jumping every time I see someone walk by on the sidewalk. I'm obsessing over whether the doors and windows are locked. The kids get excited when they see her out the window, but they're tiny and don't know that nice-lady-who-brings-us-presents is unhinged. How do I make it clear enough for her to understand and remember? How would you phrase it?

TL;DR: Neighbor with questionable mental health has gotten too attached to my young children and seems to think she can come over any time--how do I communicate effectively that she needs to back way off?