Advice needed

'Yuumi didn't match his energy and ezreal ended up hard carrying' you answered your own question right there. If signs invading you your bot is freely taking tower and denying the enemy ADC. There's a reason double smite isn't meta because it just isn't as good as having 2 people botlane

Smite perfectly, get red trinket and invest more in defensive pink wards and ask your laners to also get pinks for warding but it’s a team effort. 

More pinks, including from your laners to lock down your jungle.  Sion has no way to escape if your mid rotates and collapses on him with you or other laners. 

Consider why this isn’t a meta strat or pro play strat. 

The secondary jungler you’ll notice will always be behind in jungle camps. They sabotage themselves to sabotage you.

You get lvl 2 from any camp. The second jungler is trying to contest you - make sure your support scans all areas and checks the bushes further in for a rat hiding to smite steal and make sure you smite proper. Lay out defensive wards to catch the second jungler coming to invade. If he doesn’t get a lvl 2 kill on you - there isn’t enough resources on the map for him to keep up and he will feed enemy endlessly. I love seeing enemy shaco support as Nocturne as I can easily win duels against him over and over.

Your bottom lane should dominate 2 v 1.  As long as you don’t bleed too much in the other lanes, it’s automatically advantageous because you have a farmed adc and their adc is dominated. You’ll also have way stronger dragon control because you have farmed ADC, support and sabotaged jungler vs dominated ADC, free farmed jungler, and even more sabotaged jungler. 

If things get bad, between mid laner and your strong side bot side, you can lock down one half of the map and sacrifice your top laner and stay safe bot side taking dragons and both quadrants there. 

Watch Tilterella. He does this strategy, so maybe seeing how a double jungler thinks can give you ideas how to beat it.

Mostly, however, it’s about awareness and team coordination. Double jungle exploits autopilot decision making and opponents that are not able to work together to make life hell for one specific person. Ward, ping, and it’ll already be much easier.