No worries about the male assumption-- I am indeed male, and my spouse is my wife. I actually wrote 'spouse' because I wasn't sure if you were male or not ;)
I am married, and presently, have no kids, although this is going to change in the near future. Fortunately, my advisor also had his children while he was in graduate school, and he is quite understanding on the matter. But this varies quite a bit. My first advisor, who left the university permanently to pursue a startup (he had exhausted his sabbatical leave), told another of my labmates point blank that my labmate's decision to have children in graduate school was "the worst decision he ever made." So I've seen both extremes. What it boils down to is, yes, it's possible, no, it's not easy.
I am very fortunate in that I have an extremely understanding and patient wife. This does not mean that she doesn't have her moments of impatience, but she has dealt with my busy schedule and general unavailability (like, right now I am on the west coast of the US and she is on the east coast while I am on internship) fairly well. We took turns doing graduate school-- her first-- and so I am very fortunate in that she is the primary breadwinner. She's a doctor. My salary pays our apartment rent, and the rest of it goes into savings. Anyway, the fact that we took turns, and that I supported her while she was in school, is the reason why I am starting graduate school later in life.
If my wife were not OK with this situation, it would not be worth it, at all. One thing I realized about myself while pursuing a PhD is that I am capable of learning most of this stuff on my own. The role that professors, advisors, mentors, and [most especially] your peers play in your education is primarily to steer you into asking the right kinds of questions. This is the problem-- when you're an outsider, you don't know how to solve your problems because you don't even know how to ask them. Figuring out how to ask them has a huge search space. There are scads of ways to set a problem up, but which one is best? The people around you will take your half-coherent ramblings and sharpen them into the kinds of pointed questions that you can ask and, by turning the appropriate cranks, get an answer. In any case, the point of this is: if I blow it now, I'm OK with it. I know I can hack it by myself-- it'll just take longer.
Your list of priorities may currently look something like this:
1. Spend time with family.
2. Do well at work.
3. Chores.
4. Fun hobby #1
5. Fun hobby #2
n. Fun hobby #n
What you need to know is that the list will be transformed into something like this:
1. Do research for advisor.
2. Do classwork.
3. Spend time with family.
That's right. ALL of your fun hobbies will go away, and your wife and children will have to pick up your slack on chores. This is why you need to have a frank conversation with them. If they're not ready to do this, for the next 6 years, you should reconsider.
I am able to maintain a steady income with my side jobs, yes. But my primary side-job is providing bugfixes for the employer I left when I came to grad school. They were disappointed that I was leaving, and I explained that my time was going to be very valuable, and that I needed to be compensated in a manner to account for this. But if you aren't able to make a prior arrangement, I would not count on side-money. Research is your #1 priority, and they will pay you roughly $20-25k a year for this job. The way many of my peers do it (and I would say that about 1/4 of them are married, maybe an 1/8 have kids), is that they put their families on the fairly generous university benefits packages offered to grad students (often free health care and discounted daycare), their salaries go toward rent and food, and their spouses pick up the rest.
If your wife can't do this for you, grad school is not for you. I don't say that to be mean. You may have the intellectual capabilities to handle it just fine. But the circumstances need to be right. Learning and science can always be done as a hobby, and if you have the persistence to succeed at grad school, you will also have the persistence to succeed in science as a hobby.