My wife and I have been on 15 cruises and while I am not a single person my suggestion is that you will have a great time with your children on a cruise that is not for singles only. One of the truly great things about a cruise, is the time you spend with your family. Secondly, you will meet lots of people on a cruise and while Mr. Right may not be on your cruise, you won't be bored or lonely. Third, several cruise lines have childrens' programs that allow you to enjoy many activities without worrying about your chldren. And if you happen to find someone with whom you bond, there are times and places for romance on a cruise.
In sum, go on a cruise with your children. they will have a great time and so wil you. We took our children on a cruise when they were 11 and 6 years old. As they are grown, we still talk about the fun that we had on that cruise.
Do not hesitate to contact me for more information about cruise lines, ports of call, or other.