Am I wrong for telling MIL she doesn't have to be so mean to my little girl? (she's only 2 1/2)?

she favors the little boy over the little girl (both are my stepkids) and I don't appreciate it. she will ask him nicely to do something several times (he's 4) and with her, she hollers at her the first time and doesn't give her a chance to respond with the appropriate correction before hounding her again. I have talked to bf about this and said it's not right, can you please talk with her. it's happened on several occasions, and the last time it happened, I couldn't keep my mouth shut. SD tossed a piece of trash to the trash can from the dining room (like everyone else does in the house, including bf and myself) and she missed (she's 2, what else is expected?) MIL hollers to her she needs to go pick it up (in a mean tone) and then before she even gives her a second to take a step to go get it, she snatches her by her arm! I said "you don't have to be so darn mean to her" and it all went from there. she blew the hell up at me and started cussing and fussing with me and her other granddaughter (26) said she always acts like that. I'm like, well she asks SS nicely SEVERAL times before getting on him and doesn't ever as SD nicely and she's younger! It ended with me telling her that she's more than welcome to leave my home and I'm sorry if I offended her. She mentioned don't say sorry, bc I'm not and then left calling me a B*tch. I don't think I was out the way for standing up for my girl, I mean it wasn't anything serious. If she had thrown a tantrum or crossed her arms and pouted when she was asked to pick it up, I wouldn't have said anything to MIL, I would have re-iterated to SD to pick it up. But MIL didn't even give her a chance to react. Not to mention she always says mean remarks towards her. Was I wrong? I should have just left it at that and not fed into her screaming match, but damn, she's your grandbaby too. I want to apologize for arguing with her, but I want it understood that I still don't feel right with the fact that she's mean to her. The favoritism is one thing (buys SS candy, donuts, cookies, etc all the time and says he doesn't have to share) I can deal with that because when MIL leaves, SS has to share anyway. But being mean to a 2 yo?? Come on.