My second daughter rejected all "baby food" at 10 months, opting for "real food" cut up into tiny little chunks. She had no teeth, but managed quite well. She still drank breastmilk and formula, so I wasn't concerned about how much she was eating. I don't think they really need very much "food" as long as they still get milk in some form. So just give up on the baby food and give her finger foods and a spork or a spoon and maybe a toy to play with and have her sit with you for as long as she is comfortable. I taught my kids sign language so that they could say "all done." For us the all done sign was putting both hands up in the air. To teach this, just put their hands up when you think they are done, say "ALL DONE!" a few times and set them free. Then refuse to feed them anymore until next feeding time. That way, they could have good manners and in essence ask to be excused instead of crying and throwing food. Mealtimes should be enjoyable for all, and if her chair is not a comfortable place for her, she probably won't have too much patience to wait until big sister is finished eating.
That is another thought - See if there is a way to make her chair more comfortable - is she tall enough to sit comfortably? My daughter was so small and skinny that I folded a bath towel and placed it on the seat to boost her up. That way she could see and reach all the morsels of food on her tray.