Family is something that I really want to have in the future, however, if I want to be a pediatrician, would it give me time to still spend time with my family?

As long as you set priorities, you will find the time (in any kind of job or profession). If your priority is your family, then you have to be willing to refuse professional opportunities. On the other hand, if your priority is your job, then you'll have to miss important moments with your family and maybe become distant with them. You don't have to fall in the extreme of one or another. My advice is to identify the things that are most important for you and try to get balance in your life. 

In my case, my job gives me the opportunity to work from home. That gives me more time to spend with family. So you could always find options to have that balance.