OK, I'm going to jump right into the ugliness potential. I don't know how long this has been going on, but... If it were me, I'd start documenting that you actually offered her food and keep a diary of what the family had and whether or not she refused. If she goes back to her mom hungry all the time and complains--you might have a bit of a fight on your hands. If you've been keeping track ahead of time (and have your husband participate, too, if possible) you'll be able to head that one off at the pass.
The other thing you can try that was alluded to was to turn everything into a pizza. Mexican for the night? Give her a tortilla with cheese and let her make it look like a pizza. Sandwiches? Give her pita and make hers open faced. Both of those types of things freeze well and defrost rapidly so you can have them on hand and they won't go bad if they're frozen.
I totally agree with the other posters about how to handle it otherwise. Offer her food, make her sit through the meal with the family and if she doesn't eat it--ignore it. Keep the plate in the fridge and if she says she's hungry later, pull the plate out heat up her dinner and offer her that.
My son will go through eating jags kinda like that. I try to accommodate him as best I can, but it's easier as it's only the two of us--and the things he wants are healthy foods. Often he'll ask for something and I'll cook it only to have him change his mind later. Nope, eat what's cooked or don't. He always does after a little while, but he's only 2 so I have a bit more control over him.
The only other thought I have is I wonder if she feels out of sorts because she's the only girl. Maybe if you could spend some time in the kitchen with her actually making pizza dough or baking something else she'll come around. Something she takes part in might be more worth eating--but make it a fun activity on a day you feel well rather than one of those days it feels like you just walked in and have to be a slave in the kitchen.
Good luck to you!