FYI - I bought the single rate on Princess to Alaska this June. I got the same rate by calling the cruiseline direct as my AAA agent could offer for the same ship/trip/cabin. They charged 175%. I'm also a single mom...but kids are grown. This will be my first solo cruise, but my 11th time to cruise. I find I get better service by scheduling direct w/the cruise line and bypassing the TA (have done it both ways...50/50).
When you book direct...you can call periodically to see if the rates have gone down and ask for a refund for the difference. If you use a TA...the TA has to call and request this for you...they won't/don't care to as they're busy making money for new clients.
Hope you have a good time.