I personally think the van-living lifestyle is somewhat incompatible with doing a decent job of raising children. I qualify that with the reality that I don't think anything in the world I could do would make me compatible with raising a child, so my opinion is overrated at any value.
I may have missed it, but I am not sure the OP was planning on full timing with their children.
That being said, I know of several folks who are full time nomads, some in vans, some in larger vehicles, with children. Obviously in adolescence a person needs more privacy and space, but prior to that they need considerably less. Psychological research shows that you don't need a fixed home to have stability. Instead its stable relationships, and interaction with a small group of well adjusted adults, and some children, that important to being a functional and healthy adult.
The concept that children need to primarily interact with other children doesn't match up with research, or even the bulk of human history. In many ways it can actually cause extended adolescence (well into the 20s for some).
As far as education goes, as long as the adults/parents are willing to train themselves and select a rigorous curriculum, there isn't any reason home-schooling, or remote schooling can't work. Though I am not a fan of home schooling in general.
Many folks think that children "miss out" when they don't have the same material wealth surrounding them as their peers. All a person has to do is watch a child's enjoyment and imagination playing with the carboard box their new plastic toy came it, to dismissing that idea. Enriching, engaging, and well regulated environments are not significantly harder to create in a mobile lifestyle. This is especially true if one or both of the parents are not working full time.
It is a wealth person type of thing, but I know of 4 couples who retired in their early 40s, and live semi or fully nomadic with their younger children. It takes planning, personal skills, and self control, but it can and does work quite well.
These folks typically spend much more time and attention on their children than others who live in the same fixed home do.