Boy are you gonna have some stories to tell next year! Poor little guy. Kudos to you, you've got a full plate and you still seem to have a strong, positive attitude.
I had three close together just like you do. I never had one in a cast, but I've spent a lot of time in leg casts myself, so I can give a bit of advice about cast care.
If you can stay at preschool a few days a week then it will allow you to help your son work out solutions to his cast-challenges. (I hung out and helped the teachers a LOT when my kids were that age.) It will also keep the other two little minds active (babies dig preschoolers, preschoolers dig babies). See if there's a way you and the preschool can work something out?
Covering the cast:
Check with your pharmacy or medical supply store -- ages ago, I had a rubber sleeve that pulled right up over the cast. It had a very narrow neck, so it fit tightly round my thigh (even after atrophy). It was hideously yellow -- like a giant dishwashing glove. But it worked! Not for submersion, but allows a nearly normal shower. They also make these for arm casts -- which would be roughly the same size as a 3-year-old leg, right? I Googled a few keywords and found this site (and looks like they've improved the color range!) It's a starting point, anyway...
Otherwise, the trash bag idea works if you're very careful. Use the kind of medical tape that removes easily. No other form of binding worked for me - until the cast protector. The trick is to avoid water streaming down the leg against the edge of the tape. With the leg raised, most water will flow at a 90 degree angle to the tape-- down toward the tub, not toward his ankle. As long as you keep that angle, you're set. But make it a quick scrub.
Also, just a hint you may already know: this is the time to enlist the talents of your two-year-old. Make sure he's your 'right hand man,' able to come to the rescue of his brothers -- in return for simply mind blowing praise. You need an extra pair of hands, no matter how small -- and he needs a way to be a star. This is the age when I started calling them my 'team' and getting them excited about 'pulling together' and helping out. (Ironically, we don't play a single team sport.) To this day -- like 20 minutes ago -- that single tactic brings me help and solace in the most surprising ways. They're still my little team and they pull together most unexpectedly. :-)
GOOD LUCK -- and have fun, no matter what!