My kids aren't that small, but I moved to Africa with them two years ago (they are now 7 and 9). We are actually living abroad, not really "traveling" as in the OP, though it has provided some interesting travel opportunities as well. We don't homeschool, so any travel is tied to their school calendar as well. Even without side-travel, I feel like we have a better connection with the place we live and for that it will always be a part of us. There's no way you can get that in 90 days.

It depends on where you go, but we live very well on far less than we did in the US and it's been a great experience for our entire family in many, many ways.

I always used to read posts like this jealous of those who are unattached. While it's a different experience doing it with kids. and takes a bit more planning, it's got its own rewards (such as the impact of your children living first-hand in a different culture).