Welcome to fatherhood.
When I was in medical school, I already had 3 children. I had my 4th during the end of my 3rd year of medical school. What you have to remember is that life does not stop because you are in school. As a result, you need to MAKE the time to spend with your children. You need to figure out how things would work best for you. My wife wanted me to be home for dinner. So I treated medical school like a job. Come the end of classes, I would go home and we would have a family dinner. As soon as that was over, I went to the library to study. I wrote down all of the school activities in my calendar and made the time to go. Finally, I created "Daddy Daughter time". Once a week, I took one of my girls to starbucks or the diner and I would have a cup of coffee and she would have something. No books were brought. They drove the conversation. We talked about whatever they wanted and sometimes, they just wanted to draw and show me. And they looked forward to it.
During study breaks, I would open the camera on the computer and we would make videos. The point is, you need to be very proactive and make the time, it will not be made for you. Again, life does not stop so you need to be on top of it.
Same thing with your wife. As your child gets older, you have more options for babysitters (I had about 4 classmates that offered to babysit) and you can take your wife out (on a budget).
It's hard but doable. Good luck