For what it is worth, I think that spending time with one’s children is always a good thing. And, as long as you are going to be doing something together, I don’t see anything wrong with helping other people.
Not being able to divide and conquer can make it tough, but a couple of scenarios that always worked well for us are ‘co-pilot’ and ‘kid volunteers, parent cheers’. For me, ‘co-pilot’ was a literal sense. I’ve volunteered for programs like Angel Flight, Lifeline, and Doctors without borders. Bringing one of my children along as my co-pilot gave me time with them one-on-one (you generally only have patient passengers one way), and them exposure to helping others.
But my wife made it work en-mass and on the ground too. She’s done books and meal deliveries for shut ins for a long time, and it was never a problem to throw all or at least most of the clan in the truck/van/minivan and take them along, putting the older ones to work.
Family outings involving child volunteerism can be trickier. A good example might be youth baseball for the disabled. I’ve coached teams for many years. My older kids would volunteer and help on the field (‘coach’s’ responsibility) and my wife would have the younger ones there on a blanket playing, doing a little cheering, etc. (Mom’s responsibility). Afterwards, we’d all go out for ice cream.
That one has gone generational. One of my daughters now coaches a team, and my grandson helps while his sister sits with dad in the stands and cheers.
One last comment, don’t think you have to go big. Even small commitments can help convey to children how we feel about our Christian obligations. As I mentioned, my son is severely disabled. When he was still pretty small, he and I would always go to the earliest Sunday Mass together (less crowded meant less stressful for him). You tend to always see the same people, and I happened to offer to put away the hymn book for an elderly parishioner. I asked my son if he wanted to carry the book. This evolved into a self appointed job of picking up all the loose books and straightening up the racks. That grew into more ways that he could help at the Church as the ushers and other staff and volunteers got to know him.
Again, Good Luck!