Advice for family with only a few days

First...I don't think anyone here is "bothered by families" and you will be welcomed no matter what stage you choose to walk.

Maybe it would be good to give an idea as to which part of Spain you will be able to easily reach.
It is very easy to walk for only a few days on the Camino Francis as there is very good bus service that would be available to return you to wherever is needed.
But...the Camino Frances is long and we would have to have an idea which part you could reach without wasting too much time traveling.

Yes, just get to the Camino with as little wasted time as possible. Maybe focus on the social side of the Camino, and meet pilgrims in cafes, restaurants, albergues etc. so your children can hear the experiences, see/photograph the faces (and feet!), landscape etc. to sketch at their leisure. Nobody will mind at all, in fact families often seem to report preferential treatment. It is Spain, after all.

Even if you can't make it to the most picturesque parts of the Camino it will be fun just to join in for a while and meet a few characters from around the globe.

Buen Camino!

My experience of walking with children is that families are treated very well (mind you, it seems everyone is treated well on the Camino!)
I would second the advice to spend as little time travelling and as much time walking as you can. Perhaps DON'T finish in Santiago after walking only a few days - save that for another time when you might return and do a longer walk and then the feeling of accomplishment arriving at the cathedral is something more special.
How many days will you have?