Ladies I need some help before I go nuts.

Little details: So my MIL is a lovely person to me etc, she lives about 30 minutes away by car and drives etc. She doesn't work so is always free etc. She only visits us maybe 2 times a week(says it's because of my fiancé working a lot but that's not true at all because I told her she's welcome to come see the baby when he's in work etc). She doesn't have much experience with kids as even her son was brought up mainly by his grandma and not his mum. Now, my mum is amazing with my daughter, she raised 3 kids and kids just love her. She lives 5 minutes walk from me and we see each other a lot mainly when my fiancé is working because I'm bored sitting in the house 12h a day by myself and MIL doesn't want to visit, so my daughter is used to her a lot.

Until my baby was 4 months she was okay with my MIL, but ever since my baby literally SQUEALS AND Cries when being held by my MIL, there is always tears rolling down her cheeks and she cries so much she gets red and starts choking. It started when baby was napping in her pram and woke up to my MIL hoovering over her pram smiling at her as soon as she opened her eyes. There is no way to calm her down unless I take her back. I feel bad but I don't know what to do about this? I asked her to come round more often but she never does, and I try to sit beside her when she holds the baby but it's the same situation, she's fine if I'm holding her and sitting beside my mil. Is there any ideas on what I could do?

Another issue.. My mum out of her own initiative has given up a drawer for my baby's spare clothes that she bought herself, and she bought a travel cot and some toys and a spare bottle formula bibs etc and some toys in case she ever stayed over just so she has her own little corner. She paid for it all and she didn't pressure me into lwtting my baby stay there, she just said in case we ever want some rest she has a little bed etc to stay over. We went out for my bday and left baby at my mums, she kept updating me sending me photos etc so I was at ease. Now, my MIL keeps bringing up the subject of baby staying at hers and us going out, which we'd like to do, but she has absolutely nothing at all for the baby even though she has loads of money and a spare room. Now, I don't mind packing some nappies clothes etc, but I'm not going to take apart her cot and pay for transport just so the baby can sleep there one night. My fiancee told her to buy a second hand travel cot etc, but she never did.

We planned to go out next week with my fiancées friends, and I asked whether I should ask my mum if baby can stay over, and he said that his mum will get a bit upset cause she hadn't had a chance to babysit her yet. I calmly explained that 1. His mum never bought the travel cot she said she'll buy and she'll not sleep in bed with her (as she suggested that) because even we don't do Co sleeping. And 2. I won't be able to enjoy my night out knowing my baby is screaming when being held by her and going into a complete meltdown etc. I told him to get his mum to come over more often and we could even leave them downstairs for 2 or 3 hours while still being close to see how they get on, but she never does and I'm not gonna beg her to. He agreed with me but we still feel kind of bad. The baby won't even be calm for 2 minutes with her. She always says it must be her gums being sore, but I know it's not that at all because she's not like that with anyone else unless it's people she only saw once or twice.

Has anyone ever had a similar issue?