No one really has time to write.
There are other things we could be doing. I won't even list them down because that's just the reality of today -- we all have other places we should be, things we should be doing. If you want to write, but think that the only time you can start is when you are free from your other responsibilities, then it might never happen. Because when really will the responsibilities stop?
And if you never start, then that's too bad.
What I do instead is find out when I will have time to write, and maximize it. When I was writing No Strings Attached I wasn't a mom yet, but I was working, and had thirty minutes at the end of every workday. I wrote most of that book during that time.
When I was a new mom, and was also writing Queen of the Clueless and Icon of the Indecisive, I had an arrangement with an aunt that she would watch my daughter twice a week. That gave me about four to six hours a week, in total, to write those books.
When my daughter started going to school a few months ago, I could rely on having two hours every weekday to write. I wrote Rules We Like Breaking, 2/3 of Someone Else's Fantasy, and short story No Roses for Hannah (all yet to be released) in that time.
Now that she's on her summer vacation...I have to figure out when to write again.
The key is finding time every day, even less than an hour, and keeping at it. I write using a detailed outline, so it's easy for me to pick up where I left off. When not writing, I'm thinking of what to write on my next session. Once you do this more, you'll find yourself doing more with the same amount of time. I think I've gotten myself to a level where I can write a thousand words in a two-hour period, which is great.
So if you've ever wondered about how I "do it" -- now you know. However this is a lot easier to do when I have a solid story in mind. If you want to try to do it this way, plan your concept and outline well, so you don't spend so much time waiting for inspiration, when you should be writing.