Any advice on how to leave mom and drop her back off MC without her wanting to leave or not go in?

I'm excited for you too, hugs.

How long is it since you've been able to visit her?

My daughter always told my Mom she needed to go
to work. The word "home" was never used. I would just say, see u later.

I agree, don't take her out. I am really surprised that you are allowed to.

I learned the hard way that trips out are really disruptive and upsetting. I suggest you bring in a meal and eat together at her place while visiting there.

I look forward to bringing my mom her favorite chile rellenos again, but I can no longer take her out for them.

Time to stop the trips outside of her MC.

Call into the building and ask someone to come get Mom. Then exit the car and move toward her building while they come out to help her back in. This may or may not work. But I can't think of any other tricks at the moment. This used to happen to one lady at my bro's ALF. We would be sitting in the gazebo on the grounds, would see the daughter on the phone, then exiting her car with Mom still in it, and walking to her cottage and meeting one of the caregivers, who proceeded out to the car and helped Mom in so she could "Go with Jan and get a snack". They would then sit them both in the common dining and give them a piece of cake and tea. Then the daughter would leave. Seemed a long process, but she said it worked.

Perhaps your mom needs more time to adjust to her new apartment in MC, before family members try and visit. Your profile says she's just been there a couple weeks. I don't know how long ago you made your profile, but most facilities suggest that family stay away for a while, to give their LO time to adjust. And when you do visit, perhaps make it just once a week(which it probably still is with Covid restrictions anyway)so you and her don't have to face the hardship of her wanting to go home with you.
Also I'm not clear if you're physically taking her out and about from the MC, but if that is the case, I would stop that completely for a while, and just visit with her in her apartment. That way you won't have to fight to get back in. Best wishes.