It's not as bad as you think. We live in 480 sq. ft. and have 4 children (12, 8, 5, & 2). We homeschool too so we are here all the time. We do have a huge yard for the kids to romp in though. We live in a very cold climate, but it still works for us. We planned ahead several years for our tiny house move, it wasn't a spur of the moment thing.
If you are committed to this, it can really be the best thing for your family. We took it in steps. We downsized from a 3 bedroom 2 bath home to a 2 bedroom 1 bath apartment, then a few years and many, many trips to goodwill to give away stuff that we wouldn't need in our simplified living arrangements, we moved to where we are now. For us it's great because we don't waste money on unnecessary stuff because we honestly have no where to put anything that isn't being used on a regular basis. It teaches the kids to think critically when they want to buy something new - is this going to be enough fun, and am I going to play with it enough to make it worth the space it will take up.
Do you get along well with your husband and children? This is the key factor
to living in a tiny house. If you are the type that "needs your space", no way is this going to work. If you and hubby tend to argue a lot, there isn't really going to be anywhere to go to get away. Being honest with yourself about these issues is a must.
We've been living in our home for 3 years and it's still working great for us. If you are determined to live simply, you can do it.