That's a complicated question without an easy answer! My spouse and I are both doctors and we have two young kids. We are very happy but our lives are busy and we have a pretty high stress level trying to balance everything.
When you are a doctor, your job is different from most jobs. You have a duty to take good care of your patients and put a high priority on them. So if you are seeing a patient in clinic and they are sick, you might have to stay late at work to take care of them. If your child has a cold and is sent home from day care, it might be hard for you to leave work and pick them up, because you have patients to see.
Doctors also tend to work pretty long hours and the work can spill over into the evenings and weekends, which can make it harder to focus on your family. Here is an interesting study that shows that doctors often do work from home on weeknights and weekend nights:
Doctors have a high rate of burnout, and trying to balance work and home life can definitely contribute to that:
To sum up, yes it is possible to be included in your kids' life and be a doctor, but it is not easy and you have to really work at it. If being involved and available at home is a high priority for you, then you might want to explore other careers too.