Does boyfriends mom have a right to do this?

My boyfriend and I are both 20 years old, live together, and have a 2 month old. We go to dinner either at his grandmas or his moms house once or twice about every 1-2 weeks but it seems like my boyfriends mom just about has an issue about every other time we go. Usually after we are settled in at home after leaving, he will receive a text from her saying “i need you to come over tonight so we can talk.” It’s normally something either about him not seeing her enough or she’s upset about her son (my boyfriend) leaving her ‘nest’. I understand it’s hard for one of her children to move out, but he’s an adult and while having a baby and him working, it’s hard to deal with her being upset and calling him to her house.

For example, His mother begged us to move in with his grandmother (his side) while I was pregnant. at my baby shower in December, my grandmother (my side) talked to his mom about having an extra bedroom for any of my family for any reason, and my boyfriends mother and grandma both flipped out and left my baby shower because they claim my grandmother said we were moving in with her. I know my grandma did not say that and we never talked about moving in with my grandma, with my grandma. After they left, his mom texted my boyfriend and told him to come ‘home’ because they need to talk. When my boyfriend got there, shit went down and he said she didn’t really talk about my grandma but instead she cried about how she barely gets to see him now and how she thinks he’s going to cut his entire family out of our lives, when no one has said anything or made a reason for her to think we would cut them all out besides us not moving in with his grandmother like she wanted us to. Like I said before we have dinner/lunch with them every 1-2 weeks, sometimes more. He goes over to his grandmothers to mow her grass, we send them photos of our baby.. I don’t understand why they think that.

She says this every time she wants to talk to him. She has done this many times and has done it again today after having dinner with them last night.

He has told her he has his own family now. We can’t keep having him run to her every time she’s ‘upset’. We have even ‘surprise’ showed up at his moms house before with the baby. Is this normal? Is there a way for us to get her to stop doing this all the time?