You asked how you can do better OP, could you perhaps have a conversation with his Mum, maybe start off by saying something along the lines of 'I'm afraid I've been having a moan to BF, about how hard it is sharing a house again after being independent, and then it suddenly occurred to me how much harder it must be for you, having your DS back, and me, a virtual stranger invading your home, is there anything we can do to make things easier and more comfortable for you? She'll probably say 'no, everything's fine', in which case you could say 'I'm sure you're just being nice, but I'd really like to cook for all of us on Saturday as as way of showing how grateful I am for what you're doing for us, would that be OK?'
Also, are you pulling your weight around the house, ie, doing the washing up, doing your own washing, cleaning the bathroom, putting the vacuum round? If not, then start doing these things, if his Mum says 'you don't need to do that', then say 'No, but I want to', with a big smile on your face. Show willing, it's important.
As far as the key is concerned, most houses have a front and back door OP, just ask your DP's Mum, if it would be OK for you to have a key so that you can come and go without disturbing them. For example, if they always use the back door, say 'would it be OK for me to have a key for the front door BF's Mum? Only it seems daft to have to call you to the door every time we come in'.
I do understand how difficult it is for you to have to live with people again after being independent, but you're a grown up now, and your BF has probably just reverted back to how he behaved as a teen at home, ie, letting his DM wait on him hand, foot and finger, but for you, it's never been your home and you have to find a way of fitting in. So maybe, if for example his DM is a great cook, how about asking her if she could teach you how to cook her favourite recipe? They may be older than you OP, but they're only people, and most things can be worked out if you can just learn to communicate with each other.