So yes, every photographer is different, but I personally LOVE shooting with young kids. They have energy, they aren't shy, they are curious and goofy. Little kids literally make the best photography subjects!
The number one advice I can give is- dont try to control your kids too much. As long as they are safe, let them be kids. Let them run, play, jump, dance sing. Let them be silly, let them explore. Pick them up, swing them around, tickle them! These photos are mostly about capturing them at that period of their life.
Your job as parents is to look happy and engage with your kids, I will capture the rest. Sure we can attempt a few posed photos in the very beginning and get them done, but the best photos of families with young kids I have ever taken, is when the parents relax and let their kids run the show. Dont worry, I can keep up with them!