Complicated... Or Overthinking Things? (Coming Out)

Hello all, I'm a long time stalker of EC but a new time post-ee!
I would very much appreciate some advice from the community about my dilemma

Quick lowdown about myself: I am in a relationship with my girlfriend and have been for over two years. We're living together in the same student house, as my girlfriend is studying at the same university as me. I am confident about my sexuality, and have come out to my friends very openly ever since day one when I was sure. I really need some advice about coming out to my family, as my friends aren't too sure like me...

And now for my dilemma: My mother is divorced and lives on her own, the rest of the family are a bit up their own :***: and hardly ever reach out a helping hand to her whenever she asks for help. I live on the other side of the country at university so I rarely see her. I'm currently at home with her for the summer though and I definately want to come out to her, I'm fed up of living a lie with her about my life and I feel like now is the time. I care not about my father, he's an :***:. The reason why my mother is so fragile is because of him. Anyway that's a story for another time!

The problem here is that my girlfriend is the one who convinced me to go to university, and my mother hated her for it because I think she was scared to be left on her own at the time (she's fine about me being at university now and we talk every week when we can). I'm unsure about how she feels towards girlfriend now, some days she'll ask how she is (as far as my mum is concerned girlfriend is my best friend) and some days when I mention girlfriend she seems pretty meh about the fact that I brought her up.

I have no idea how she will react to this. When arguing with her about university, she threatened to kick me from the house. But she's so excited to see me right now as it has been a whole year since we last met up and has been loving and caring as usual. My mum is also borderline medically depressed due to issues with her neighbours... I haven't yet told my girlfriend about wanting to come out, I want it to be a surprise for when I see her after summer because I know she will be so proud of me for doing this, she knows how much I fear what could happen to the relationship between me and my mum and that I wanted to keep things a secret. (I think my cat can sense that I'm getting upset because he's just come and sat himself right on the edge of my laptop and is staring at me, lol!)

I have a few questions that I wish to ask and would appreciate the advice and opinions of everyone, positive or negative:

1) When should I tell my mum about my secret relationship/sexuality? Now at the start of the 5 week break so I can try to fix things with her, or at the end so I can retreat back to university and give her all the space that she wants?

2) How should I go about telling her how I feel? I'm thinking about writing her a letter as I wish to become a freelance writer when university is over, and I find it easier to write my feelings down rather than stammering them out. But I feel that it would be a lot more personal if I tell her face to face...

I'm very sorry if I sound as if I'm rambling on and on!! Again I would really appreciate some feedback from you all! Thank you!!

<3