I'm a WOHM, but I think you and I have the same syndrome.
The other day I was at a meeting about an upcoming camping trip for my 6th grader. I'm a little worried about my son sleeping outside at the height of what's asthma/allergy season for him, so I asked if I had the option of picking him up in the evening and returning him in the a.m.. They said yes. Another mom asked the same thing (different reason) and so we began talking and I suggested that possible we could carpool. She was delighted, and told me how she was a single mom and she had to work and how not making the two hour trip in the a.m. and p.m. would be great for her.
Then I got home, and my DS told me he didn't care how sick he was, I was NOT embarassing him by picking up up.
The first thing I thought was "well, I should probably call the mom and tell her I'll still pick up her kid, I mean she's a single mom, and she's got these special circumnstances . . . ." Now, I should mention that I'm a single working mom too, so this was totally illogical, but this is the way my brain works -- I take on everyone's problems to solve as if they were my own.
So just say no. Or tell her you need her to pay, or do whatever meets her family's needs.