DIL / MIL relationship

Sorry the post ended up quite long :-/
I love my partner very much and was hoping for a good relationship with his mum. I've always got on well with boyfriends mums before and with my own living so far away I was hoping for more of a relationship with my mother in law. Some history as to why I'm struggling having a relationship with her...
My partner had been on his own for several years before we got together and his mum was used to having him at her beck and call. I met her for the first time when she decided to let herself in my partners house without permission whilst he was at work (yes that was awkward). I've always been very independent and quite a private person so she was asked not to let herself in but continued to do so and when we were away do diy that she thinks needs doing (unfortunately not very well). We asked her several times not to and each time she promised not to do it again but did. If my other half gets firm and discusses taking the key away she'll cry and always goes onto the subject of a hospital appt (she's been in remission from breast cancer for 7/8years now and has had a couple of hip ops).
I feel I have made an effort with visiting her and trying to be friendly, she only lived a couple of minutes walk from us and wouldn't visit when we were in. I've made cakes to take round and she has handed them back to me to take home without trying. After one op I made a quiche (I know she eats quiche) and bought her food so she didn't have to go out, but she refused it and told me she'd rather have left overs. I host a lot and cook for other people and my food always goes down well. I recently made a picnic for an outing out, we phoned her to check all the food was okay for her, yes it was. She then bought her own food and wouldn't eat what I'd made for us.
In January we had a daughter, we decided to keep her name to ourselves until she was born. On Christmas day MIL started shouting at me because of this and FIL had to step in to stop her. When baby was born we would agree a time for her to visit but she'd just turn up whenever she wanted and let herself in. After the first week we were told it's time we started going to her rather than her coming to us. We told her she is welcome to come to us when ever she likes just text to make sure we are in and she has been asked to knock at the front door. Now she makes a point all the time saying 'o well I won't see you until such and such day then' we say come to us before but she won't and on the rare occasions she does makes a huge deal about not being allowed to let herself in. She also keeps telling me my daughter has far too many clothes, I shouldn't buy her things and turns up regularly with a bag full of clothes. She also refused to spend any longer than 5/10minutes with our daughter.

A few weeks ago we moved into a lovely house that my partner and I jointly own (only 5mins drive from MIL). My partner is also fed up of the letting by herself in so decided not to give his mum a key as he's worried what she'll do to the place whilst we are out. The last 4 weeks my mother in law has been visiting a lot, and been much nicer to me. No nasty or snide comments. She is also now regularly asking to look after my daughter. I'm really struggling to trust her and know if she genuinely wants to make an effort now or if it's all just because she wants to babysit. I would like to repair the relationship but I'm finding it very difficult, I find I'm just waiting for the comments to return or a reason why she's changed. Any advice??