Welcome to the family, Victoria!
I am not aware of any mostly "singles"/"single parent" cruise ships although most of the cruise lines today have "day camp" activities for kids of all ages where your children can stay busy, have fun, explore & learn, creativity and talent focused structured schedules that I would like to join! It's so true - "youth is wasted on the young"! They will be out of your sight in safe environments most of the day, leaving you free to mingle and get acquainted with other guests - ask questions, strike up a casual conversation, hang out by the pool, or sun deck or any activity where other adults converge and make a connection so you can start the information extraction process - the go in for the KILL....demand to get hooked up!
No, really, in the evening activities for adults, you will meet other people and hook up....the ships have night babysitting for your kids after they have become exhausted from the long days events. Roam from one club to another until you make eye contact with an unsuspecting beast of prey...or just approach the person who looks like he's lost and lonely and offer to buy him a drink (then make your move)
Of course I am being silly........it's my way of easing into conversation without agenda or commitment! You need to have a point of reference as I stated in the first paragraph of this msg. Also, search all msg boards here and post a "new topic" - initiate a message that will draw other members to your topic and offer suggestions and sound advice. If I can help in any way, please reply to me via e-mail or private message to maintain your privacy off the common post board. I don't mind and I would guide you with honesty and from my own experiences.
Get started, girlfriend.....time's a-wastin'!