Is it me or her?

I am going back to work soon and my MIL has offered to have baby for me. I really just don’t feel comfortable with it and I don’t know why. Well I guess I kinda have some reasons but is this a me problem am I being overly sensitive here? First of all she has absolutely nothing for baby at her house not even so much as a pack of baby wipes she has literally nothing there for her. I keep sending her messages saying oh I’ve just seen X for sale in the charity shop it would be useful to have at your house but she doesn’t reply to me. My own mum has bought pretty much everything a baby would need to keep at her house so when I go to visit now I don’t really need to take anything other than her clothes. I also feel like she doesn’t even really know my baby very well, despite only living a very very short walk away she only sees her about once every 2 weeks and I never speak to her in between that, well sometimes I text her but she doesn’t reply to me. I have found her to be quite disrespectful to me in the past as I was planning a home birth and she was so against it she made it quite clear. I didn’t end up having a home birth which she was very happy about. Also, when baby was newborn I asked her to come over to look after baby in my house (I made the in MY house but very clear) as I wanted to clean we arranged a time and then when the time came she rang me said right im coming over now but I’m taking baby back to my house with me and I said no you’re not she’s literally 3 weeks old she’s not going anywhere and so she never came round. I’ve never asked her to look after her since as I just feel like she will try to take her away from me. I could go on and on about things but I guess I don’t particularly get on with her but am I being overly sensitive with it and I should just let her have baby when I go back to work? I am self employed so I can take baby to work with me it’ll just be more stressful