I've dated single moms and even lived with two of them. Just dating (and fucking) single moms is great and the sex is probably the best you will ever have. DO NOT LIVE WITH THEM and [[[DO NOT EVER EVER EVER MARRY ONE!!!]]]
Cohabiting with them is bad news.
1) The sex drops off at least 25% as soon as you move in together. After 6 months another 25% and after a year or so no sex at all or very infrequently.
2) You will always be the outsider. She and her children are a family and they will see you simply as the guy banging their mom.
3) She will expect you to pay for dinners, birthdays, Christmas presents, vacations, etc, for them even thought they aren't your kids. You will also be required to go to graduations, sporting events, band concerts, etc, even though they will always want pics with their mom and dad and not you.
4) In many states you could be required to pay support for her and them later especially if they don't already have a dad paying child support. In some states now simply cohabiting with a woman OR just dating her for years and going on vacation with her could force you to pay palimony.
It's best to just get the sex until she pressures you to move in or get married and then cut her loose. Make sure you don't get her pregnant.