I actually started getting more done once my daughter was born (well, not at first, after about 8 months or so).
I only had an hour or two when she was asleep in the mornings or evenings when I wasn't, but I was really focused and productive during that time because I knew that was all the project time I would get.
And I totally agree with the other posters. Sleep is super important, you want the time you do have with them to be quality time not grumpy time.