Pasting below from a user who PM'd me to remain anonymous:
I'm fellowship trained, male ophthalmologist (married to another physician) who had one kid going into residency, another child early in residency, and a third during fellowship. My residency program had many kids among the residents; however, my fellowship had almost none among the residents, but a handful amongst the fellows.
The overall daily schedule didn't vary too much; however, the key is that we had hired help. We had a babysitter/nanny that came to our house at 6AM and took the kids from there and then also picked up the kids from school/daycare at 3:30PM and stayed until 5:30PM (or until one of us got home). In general the nanny would take care of the older child(ren) and we would take the baby with us to drop off at daycare on the way at 6AM. We would generally wake up at 5AM and get the kid that was coming with us up at about 5:30 and them/us out the door at 6. The kids who the nanny watched could sleep until she got there, but usually would wake up before we left and hang out.
In the afternoon it was pretty much the reverse operation. For feeding the baby the wife would pump and then the baby could eat whenever needed. Between my wife and I it was just whoever could do whatever, whenever. We also needed significant help from family coming in and staying with us for sometimes weeks at a time to help when one of us was on an away rotation. For call we generally went off her call schedule and then I would work with my co-residents to switch my calls with them on conflicting days.
As to studying/reading: well, you just have to find time to do it, usually after the kids went to sleep. We would also try to give each other a half day on the weekend where the other one would watch all the kids and one would leave and go study. If it was close to inservice/boards time then the other one would take the kids much more often to allow the other to study.
Finding daycare/help can be extremely difficult if you need extended hours. In general you will pay extra and may have to look outside normal modes of care for help. I know some have had an au pair, but there are some significant work hour restrictions for them. Depending on how old your child is can also make things difficult. Care for a newborn can have very long waitlists!
The one thing that makes a HUGE difference in how things go is if it is a dual working parent family or not. In a single working parent family the care issues are much less of an issue; however, money is a bigger issue and I have also seen resentment seep in from the non-working parent in regards to the hours spent at work and inability to help as much with the child. In a dual working family the biggest issue is finding/arranging care that meets the vagaries of a medical residents schedule. Try making medical appointments for your child...they are all during the same hours you will work! What happens if your child is sick and you are both working? You will need some sort of help, whether it's family, friends, or hired, you will need it. If I had it my way it would be great to be able to live near family who are interested/willing/able to help.
Overall, there really is no "good" time to have children when you are in medicine. Many think waiting until after residency is good; however, immediately after residency (at least for ophtho) you are worried about Boards for 1-2 years. At the same time you are trying to start a practice or make a good impression and you probably feel bad taking the time then. After you are settled into a practice you have your own patients that you hate to leave for the time to dedicate to a new child. It's really never ending and then at some point you realize you are getting older and if it's not "too late" already you realize that the chance of having more than one kid is even more remote. My opinion...you have to have kids when you and your family are ready to have kids. Residency will deal with your absence, work will deal with your absence, all the other people will somehow continue on with the work.