Whatever you decide I think your idea of "traveling the world" with your kids is a good idea. When someone says they plan to travel the world, they don't normally mean 125 countries as mentioned above. According to the World Atlas there are only 189 - 196 countries in total, depending on the definition of a country.
We didn't exactly travel the world with our 2 kids but we did rent houses or condos or cabins etc, for holidays of 2 weeks at a time in countries in Europe and the Caribbean, plus 2 month long vacations with them in Australia. They are in their 30's now but still talk fondly about those trips, and now enjoy doing their own travel. (Last year DD visited S. Korea, Hong Kong and Japan with her SO)
We didn't exactly travel the world with our 2 kids but we did rent houses or condos or cabins etc, for holidays of 2 weeks at a time in countries in Europe and the Caribbean, plus 2 month long vacations with them in Australia. They are in their 30's now but still talk fondly about those trips, and now enjoy doing their own travel. (Last year DD visited S. Korea, Hong Kong and Japan with her SO)