I won't comment on the lifestyle-type issues. Every family is different, and you probably aren't looking for life advice on a sailing board.
Here's something boatwise to think about. A catamaran. Many traditionalists think them anathema, but for cruising, particularly with kids, it's a very good platform. I'm a monohull sailor myself, so I'm speaking from limited experience (not none, but not extensive) and a decent amount of research (we're considering a cat for our next boat for our own sabbatical a number of years out, but we haven't yet decided, and still haven't decided whether we even want to give up our Miracle). Here's some of what you get with a cat:
1. Privacy for all. The typical owner's version layout puts an owner's master in one hull, and then the other hull has two private cabins, on opposite ends, both sharing a head or some with two heads. If you've got two kids, particularly of the opposite sex, you can't do better than that. All of you will having cabins in opposite ends of the boat with plenty of space between you. Don't underestimate that.
2. Level. One of the biggest draws to some. No healing.
3. Stability. This is related to "level," but a little different. The boat won't roll. It will have a different motion, and maybe a little herky-jerky, but it won't roll and have exaggerated yaw. That motion often (not always of course) is what makes people sick. It may very well help limit seasickness. Likewise, if you're in a rolly anchorage, you'll be stable while all the monohulls are all over the place. I've been there, and know I will continue to be, and that part ain't fun.
4. Space. The cockpits are huge, the saloons are huge, the decks are huge. If you're living aboard and cruising, you'll spend the overwhelming majority of your time on the hook, and having that kind of space will be very important, particularly considering you will have kids.
5. Speed. If you really load down a cat it's performance will suffer greatly. But, if you're reasonably careful and get a boat designed to handle the payload you plan to have, you will sail a lot faster. That means less time at sea, which means you will have less exposure to adverse weather.
6. Draft. Most cruising cats draw 4' or less. That will get you into a lot of places you wouldn't be able to go in a prototypical monohull. If you want to go to the Bahamas, that's a key consideration.
There are other plusses, and certainly there are minuses, but this thread is not about cats v. monos.
Just something to consider. Here's a link to friends of ours who sold up and went cruising on their Manta 42 with two kids. http://mapsjohnson.com/index.html