I like Bliss36 and Babbot1's answers.
I assume you would need to rent some storage space for your household "stuff" that would be in the way on the boat. The less stuff on the boat, the better.
Laundry is often a hassle when living on a boat, especially if your moving around to state parks / beaches.
You said you have an escape plan (you said you can rent a house when you get tired of this arrangement). Is your wife is up for giving this a try (I wouldn't push anyone into this)? Are you working during this time period, and your wife is stuck on the boat? You will need to learn new ways to communicate and give each other space and recreation, while still taking care of two toddlers. You will need baby sitters that can safely deal with boat life...might need to train them, and/or baby sitters that can take the kids somewhere else.
Sounds like an "adventure" you would never forget. Just make sure your marriage and family can survive it.
...and start a new post to chronicle your adventure if you do it.

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"Knot Easy" 2000 Horizon 240 Volvo 5.7GS /SX
tow: 2017 Honda PILOT EXL-AWD
prev. boats:
'87 Chaparral 198CXL 4.3 OMC Cobra
'69 Jetstar 16ft Ski Boat, 115hp Yamaha
'68 Aluminum Jon Boat, 3hp Sears
'64 Water Wings