Baby crying with MIL

My baby gets really upset when his Grandma comes to see him. She has to go into another room while I calm him down - even then he'll be very unsure of her and cling to me for dear life. My mother in law is naturally very upset about this, and I do feel bad for her. Anyone else been through something similar and have any other tips? I have a challenging relationship with her but can't deny she dotes on our little one. I'm also trying to navigate her expectations - she's historically refused to come over unless we were going out and leaving her to babysit. But as little ones got older, it's just not feasible. She's in her mid 70s and her mobility isn't great - we've had a few near-misses which she definitely downplays. She made a comment that my son was crying because I don't invite her over enough, but will also say "what's the point me coming over if I'm not babysitting" 🤦🏼‍♀️