If you don't qualify for family boarding (which would solve the problem), the official Southwest answer is either everyone boards at their own position or you board with the last position.

A couple of things:
If anyone in the group has a disability, that could qualify you for the extra time group that boards between A and B. Please don't lie but also non-obvious disabilities like ADHD can qualify.

How old are the kids and how experienced are they as travelers? My 10 year old boarded by himself in A group yesterday and saved seats for me and his sister (we were in late B's), but he has also been flying at least 2x per year since he was a baby. So physically boarding the flight is pretty do-able for a kid; the biggest risk is that they would be boarding after you and have a small chance of getting left behind if something went wrong. If they are confident travelers and (especially) have a cell phone, I wouldn't worry too much. But it would also depend on how complicated the gate area is and how many flights are boarding nearby at the same time.

Finally, this won't help this time, but based on your numbers, it looks like you checked each of you in individually, in sequence on the same device. In the future, it may help to have all 3 pulled up at the same time on different browsers/devices so that you can do them almost simultaneously.