DIL / MIL relationship

While you were still living at the first house you should have been stricter with her regarding her letting herself in and doing DIY!
I would have told her if she did it just one more time we would be getting the locksmith in and she would not be getting another key. If she thought you were bluffing then gone ahead and done it.
It does sound that she is quite controlling and likes her own way, having her son at her beck and call for quite some time before you were together is probably hard for her to get used to now .....she has to learn to share him with you in the nicest way possible way if you are all to get on well together.
If she says things such as " I won,t see you again until ? ......" smile and say yes that's right and don,t let her guilt trip you into other arrangements.
This lady needs to learn she can,t have her own way all the time ...the dynamics have changed now and she has to change with them.

What does you DH think about the babysitting? Personally, it would be something I would be wary of because this is obviously a manipulative lady who will eventually have your baby's ear to bend and mind to play with. I have a mother like that and I am always happy for her to see my children but never without me or my OH being present. She just can't help herself, she has to undermine me or my husband at every turn whether they are her real views or not. It just isn't worth it the freedom of having an hour off!
Well done for the key business, nicely played. Just don't ever give her a reason to borrow yours because before you know it she'll have a copy!
I think any decisions you make should be made with your husband so you can stand united when the going gets tough. It sounds like he has her measure so I am sure you can work as a great team.

I've no idea why your partner didn't change the locks in his old house. He would have known what his mum is like with the waterworks being turned on to get her way.
I wouldn't let her look after baby and anyway, she might end up nosing all over your home and start changing things around in your absence.
The MiL from hell.

It's amazing what majic a DGC casts over a once difficult MiL. (Still say NO to the key tho).

However nice this woman is too you....the damage has been done, and I think you know what her true feelings are....she seems a very jealous woman and seems to be being nice because it suits her....Don't EVER let her have a key to your new home.

Oh my goodness, does this lady not know how lucky she is, to have a daughter-in-law like you? She has well and truly overstepped the mark and still you accommodate her. It's such a shame that the mother-in-law/daughter-in-law relationship has to be so difficult, but it very often is. I had a lovely relationship with my daughter-in-law. I always waited to be asked to vist, or to babysit and never interfered. Now that she and my son have separated, she has cut all ties with me completely and will not allow me to see my grandchildren, even though this is upsetting the children, in addition to them already being upset by their parents'
separation. You are ver good to keep doing what you are doing Alibr, I hope that she comes to her senses and I hope also, that your partner appreciates all your efforts, with his mother. It is not a competition between MIL & DIL for son's affection.

I would recommend you spend time with her on your own, so you could have a chat about all the issues you both seem to have. Make it somewhere quiet and where you cannot be disturbed. Put the kettle on and sort it out. Do give and take.
Talk it out, you achieve nothing by staying quiet.
Be open and honest and remember it is a two way process, she probably has issues too and does not know how to get through them.
Good luck and be patient and kind.

I find your house choice puzzling. A friend and husband in a similar situation deliberately bought a house an hour from her MiL, which was also difficult to access by public transport (MiL didn't drive), to stop unwanted intrusions. They then had a happy relationship with her because they were able to see her regularly, but could control when and how much.

Why on earth didn't you change the locks on your previous house?

No babysitting until she has shown you she can respect all your boundaries.

It does appear as though she is behaving to gain access. And that isn’t a good thing because she will still openly disrespect you - and now she will be given a chance to do so in front of your child.

I would not trust her yet.

Your mil sounds like a nut job. Would you knowingly let a nut job care for your child? I would say no.

Who is your childcare if/when you return to work?

Thank you for all your comments, sorry it's taken me ages to reply.
@Diktat DD is going to nursery near my work, which is an hour commute.
@Jtjade unfortunately I think the time for a sit down conversation has gone. Some of the behaviour I didn't mention before was I've witnessed her lie about a conversation she had with my BIL to cause trouble with him, my partner (partner and BIL have never gotten on) and FIL. I've also witnessed this behaviour to cause trouble between my partner and FIL. This hadn't happened for a while but has started again and means I don't want to be on my own with her as I don't know what I will have apparently said or done. The really sad thing is I'm afraid my partner would believe her over me. (Partner issue not MIL I know)

My stance now is I've really just given up. I've just asked it be mentioned if she is coming round, that way I'm prepared and can have jobs ready to busy myself with so im not around her much. She's started also turning up unannounced, if my partner's not at home I pretend I'm not either and won't answer the door. I've also made it clear if I'm not expecting someone or a parcel I won't be answering the door on my own. I'll be civil but I've lost all energy and will to make an effort. The snide comments are slowly returning and it's really sad but if I find my partner is there to witness them and doesn't start standing up for me I've lost my energy in my relationship too I know I should accept my partner and MIL for who they are and learn to accept that my partner just doesn't want to stand up to her but he is aware it upsets me and im struggling to accept the fact that doesn't make him do anything about it. I have a gorgeous daughter and she's the one my time and effort needs to go into now and making sure she is happy and not seeing an unhappy mum.

P.S. I part of me would have loved to move further away but jobs and house prices really limited options.

Agree with other posters. Your house, your life, your family, your rules. Obviously the never ever giving mil a house key is now clarified. Mil has already demonstrated that she will abuse that privilige. Make it clear that you will not open the door unless she has checked with you first that it is convenient to visit. You do not have to explain to her why it may not be convenient. Allow babysitting at your house only when, and if, it suits you.

As you say the time for cosy conversations with mil has now passed but it is very important that you do have these conversations with your husband and that he understands the importance of supporting you totally. Your mil will sense any disagreement between you and use it to drive a wedge between you and your husband. Hopefully setting and consistently enforcing limits on your mil's behaviour now may save you years of conflict and pain. Your mil is a bully and bullies need to know when they have overstepped the line. Good luck. ?