On average, except in the summer, you can expect to sail at least a few days every month. These trips can vary from one to several days. Sometimes you will sail on Monday and come home Friday. Other times you will come home the following Friday (i.e. a two-week trip). At least two or three times a year, you can expect to make a 59 day trip on an exercise or patrol (a whole hockey sock of benefits kick in at 60 days, so we tend to cut it short at that point). At least one ship, from either the east or west coast, is usually away on a long deployment (usually about six months).
During the summer, the ship will likely take a "leave period" where it's alongside for at least six weeks in order to allow everybody on board to take at least three weeks leave (half the ship's company at a time). They may also tack a short work period onto this so that some folks may be able to get more time off or they can least have a little more flexibility as to when they actually take their leave.
Can you be a single parent? Yes, but you do have to plan for it and be organized. I had a sailor working for me years ago who was a single mother with a young child. She was on of the most organized people I've ever met and had very strong family support system (kid usually stayed with her brother's family).