Two of us in our family. Where we ended up was to both train on venerable old 2 seat Cessnas, then when one of us qualified we bought the tourer that met our needs and then did the differences training so we could fly it. Another factor for us was that a big 4 seater picks up a crippling insurance hike if it's used ab initio training.
Provided it's legal, then your proposed way forward also sounds fine. I think the point about about picking an aircraft that is easy to fly (which the previous ppruner made) is crucial. You want all three of you to get through the course, so pick an aircraft that makes it easy. You don't want an aircraft that immediately stops flying and dumps you on the runway if you get a tinsy bit slow for example. Other ppruners will doubtless be able to give some good advice on this thread.
I hope you have a great time. But stick with it. I think it will be tough for three of you. One of you will doubtless be much better at it than the others, one won't like it that much and the other probably won't be able to find the time to do it (or equivalent difficulties). I'd recommend you start out with the clear intention to support one another rather than compete. One more thing. If one or more of the three family members is a son or daughter, do remember the rule. You can complete a PPL in 45 hours provided you are a teenager. After that simply add on your age to find out how long it will take to qualify. I was in my forties and yes, it did...