Quite frankly, I find doormats like the LW to be so irritating that I have to walk away from the screen just to compose a reply.
My response would have been to ignore the pointed looks the first time, and if the other mom point-blank asked, I would simply say that I had only budgeted to cover my own expenses, and suggest she call her DH or someone else to provide the funds for her to cover her own expenses. Repeat as necessary (since it appears to be a regular occurrence) until she gloms onto some other person who has hopefully learned by the example set to not be a doormat either.
Being thought cheap? That doesn't even make sense to me because LW is covering her expenses. I don't care how small the amount is, I don't cover for casual "friends" (most people seem to use this word far more loosely than I would, I would consider the other mother to be an acquaintance).
Who lets this become a giant thing that goes on for weeks and writes a letter to a help page on the internet about it?
All she has to do is say 'no, I can't pay for you this week', and be done with it.
Once, I can understand. Twice....okay, if you're put on the spot. But by the third time, I would just have to think that the LW had been stewing about it long enough where she would blurt something....anything....out of her mouth. Stammering. Some feeble excuse. Something. NOT let this person get yet another free lunch off of her.
So I'm thinking that there must be something else at play here; some weird dynamic, some Junior High clique that never grew up, or some interesting power base. To me, the whole thing just sounds so bizarre that the moocher would specifically target the LW like that, but just apparently LOOK at her and get her to comply. Several times. It sounds so.....science fictiony. Like mind control. Bizarre.
But yeah, Mooching Mom needs to be told a very simple, straightforward, "No." (And then the LW needs to look at her and laugh, like she thinks MM is crazy for thinking she can continue to pull the same stuff, because she is.)