Oh lovely, you sound so sad and at the end of your tether. I want to give you a hug!
Ok, so baby steps.
First of all, your DS is TINY! Teeny tiny and totally reliant on you for all his needs. My middle child wouldn't go to anyone else for 18 months, but when all of them were that little, they just wanted me. My DH always found this stage difficult because they just wanted to be held by me. I bf them all and I think they found the comfort in the smell and the familiarity.
BUT - it didn't last. Probably around the 3 month mark, slightly different with each child, but they all became a lot more interactive, interested in their surroundings and a lot happier to go to daddy. They started smiling, which helped with the bond with DH and they didn't need milk every 2 minutes, and their sleeping patterns became more regular. Hold on, it will improve.
Things that you can do proactively to help. Say to DH - we need x from the shops. Please take DS in the pram to get it. He may scream all the way there and back, but in reality he'll probably be lulled to sleep by the movement of the pram. It helps if you've just fed him and he's sleepy. Give him a purpose.
Then - I need to take DD for a haircut, shoes fitting, we're going to the park for half an hour. Think of things you two can do together that are fun. Say you need this time with DD and it will only be half an hour. Then escape. It will give DD time to herself with you and help massively. No excuses with DH. Tell him you need this time with her.
With the Nan, boundaries are all. So next time she comes, give her things to do. Here, please can you hold DS whilst me and DD make the tea/change her nappy/read a book. Plonk him on her knee and make a swift exit with your DD.
When she's going say, we'd love to see you on xx. Set the rules yourself. If she says I'm coming over tomorrow, say I'm sorry, that's not convenient. But we'd love to see you on Saturday. Then stretch the days out until it's something that works for you. Say you want to establish Sunday lunch with her on a weekly basis, or Friday night film night, or swimming on a Saturday. Again, think of the way it's manageable for you and baby steps.
Re Christmas, I would park the discussion for now. You're tired, and hormones are flying around your body. I remember feeling like the world had ended about 6 weeks in. I don't know what happens post pregnancy, but for me it was a really tough time. Again, I began to feel much more in control around the 3 month mark.
Don't talk to anyone about it. Your mum or your DP.
Make a decision to broach it in September. It gives you time to come up with a plan that suits you, and your routines with your DS will be a lot more established.
In your position, I would be tempted to invite your mum and your nan to you for Christmas. If she says no, she wants to be with the aunt's family, say that's fine we'll see you on boxing day.
When the time is right for the discussion with DH, say I'm not prepared to leave mum home alone. This is a plan that works for everyone. Mum can stay over on Christmas Eve and nan can come for Christmas meal, which we'll have at 4pm. (The reason for this is it's a fabulous time to have a main meal for little ones. We got into this when ours were little. Close enough to their normal tea time, and meant that we could have our starters whilst they played (no interest in starters) and then all have our main meal together. We'd then feed them a child friendly desert, and they'd crash around 7pm, when we'd have dessert).
Tell your DH that it's no fun for anyone if the kids are dragged around on Christmas Day and this way everyone can have naps when they need them and go to bed in their own beds when they're tired.
You're not saying no to nan, but you're letting her be involved on your terms. It sounds like he doesn't care about the aunt and family so they can sod off, and nan can choose who she wants to spend Christmas Day with.
Hope this helps a bit lovely, but leave contentious discussions until you're a bit more recovered and have the stamina to put your foot down.