I've dated my fair share of single mothers. Here are some red flags...
if she is constantly talking about her 'baby daddy'. Red flag.
if she is openly admits to needing a father for her child. Red flag.
if she is trying to get you meet her child and spend time with the child right off the bat. Flag on the play.
if she says these words "me and my child are a package deal". Flag.
if she's always griping about how her 'baby daddy' doesn't take care of his child. Flag.
if she's always broke. Or asks you for money, or ask you to buy things for her kid. Flag.
if she ever ask you to babysit. Nuclear Red Flag. :nono: Eject immediately and don't look back.
Some other tips....
1. You are her vacation from the messed up life she's in. Keep it that way. You don't date vacations, and you don't go on them every day...you just enjoy them when you can.
2. You play the role of the swuave player with a heart of gold, but you don't get sucked into her life. The point of 1. is to take her out of her life, let her enjoy life like it was before she got knocked up.
3. You do not spend time with her child. I repeat, you do not spend time with her child. You do not grow attached, you do not think of 'being a family'. You especially don't do this inside of the first year or two of knowing her.
4. You will have other girls. She expects you to have other girls. She knows her market value is low, and if she's the only girl on your radar then your market value is lower than hers, instant power shift.
5. You will not become needy or clingy. Her children will always be ahead of you so becoming needy or clingy will be even worse than with a childless woman. It's the quickest way to ruin.
6. You will not see her on a regular basis. i.e. several times a week. You will put her in the rotation of once, maybe twice a week.
7. You will not take her out on expensive dates. You may take her to the movies or some applebees type place every now and then, but there should be at least a 3-1 or 4-1 ratio. For every 3 times she just comes over and "watches a movie" you MIGHT take her out on a real date.
These have been some of my lessons I have learned from experience. take what you find useful, discard the rest. Good luck.