AITA for giving my son’s girlfriend a budget for the dinners she’s making?

My son (23M) graduated university back in June and he moved back across the country to live with us since he found a job in the area. He’s been in a long distance relationship with his girlfriend, Carmella (21F) until October. She initially took a semester off from college and was living with her mom. However, she’s decided she’s not going back. Her mom said she would have to move out and she had nowhere to go. My son is moving into his own place in January and had invited her to move in already, saying she could get a job in the area. However, she needed to move out sooner, and they both asked me if she could move in. I agree. Neither are paying rent as I personally don’t believe in charging my kids to live here, so it felt wrong to charge Carmella any. I just asked that they clean up after themselves and be respectful of everyone. They agreed. Carmella moved in after Halloween and she’s been a joy to have here. She’s still looking for a job. Most nights, she’s offered to cook dinner to give back to us. I’ve always told her it’s not necessary, but she insists. She’s a good cook, so I tell her if she wants to, have at it. 

A week into her living here, she mentioned wanting to make a certain dish but we didn’t have the ingredients. I offered to give her my card so she could buy groceries. Since then, it’s become a regular thing. I didn’t mind it initially. She picked up my groceries as well, and it seemed to be a good deal all around. But then a couple of weeks in, she started wanting to make multiple trips a week and buy things that I normally wouldn’t budget for on a regular basis, such as steak and seafood. I asked her on Sunday when she went to the store to please get everything she needed in one trip. She said okay. I thought that solved the problem.

Cut to Monday night, and we finish dinner. She and my son are talking while I’m doing the dishes. Carmella mentions wanting to make steak on Thursday. My son says that sounds good. Carmella says she’ll have to go back to the store. My son turns to me and says “Mom, give her the card.” I tell them no. I say I already gave her money to go shopping on Sunday and told her to get everything she needed. I also said we can’t swing everyone having steaks this week  (6 people in the house), but maybe I can make them for Christmas dinner. I then go on to say if Carmella wants to keep cooking for us, which I appreciate, I am going to put her on a budget. I apologize for not doing it sooner. Carmella looks upset and my son seems offended. Later on, my son tells me I “embarrassed” Carmella when she’s just trying to be nice. I said I appreciate her cooking dinner, but she’s doing it on my dime, and I can’t afford this. I pointed out he’s free to give her money to do this. My son pointed out they’re only here “a few more weeks”, can’t I just make “my guest” happy?

Am I really in the wrong here?