She is a single mom as well and always posts pictures of her and her daughter. She's super into fitness as am I.
They were always girls I just met behind a keyboard in my comfort zone.
Facebook is the Devil. But it looks like that's all you've got, so.....
You've already done your stalking homework. Start IM-ing her with her. Take it nice and slow. Don't send her a message telling her she's hot any single mom with 3000 friends, has been told she's hot a few thousand times. Look for a post maybe where she's doing something fitness related with her ankle biters, and comment on that like "That's cool, mom works out with the kids!"
Hot single mom's may get some attention, but they really don't have much time to get a dose of [D]. Find the right time to start a longer conversation chain through comments. If she keeps writing back to you, then she must like talking to you. Look for her after kiddie bed time. Don't mention that you know what her interests are from stalking her page. Just try to mention something that you've just seen. Don't over message. One message. Wait for a reply. If she replies and starts asking you shit, then she wants to keep it going.