I'm so sorry for your loss, you've got it tough.
Not quite the same as your circumstances, but my mum died suddenly when my lo was 4mo and ebf. I'm an only, mum was single so it all fell to me. I'm not sure how I survived, but I have somehow muddled through the first year and a bit since. I'm not sure if it's what happened, but my lo just wanted me all the time too, so whilst others tried to help it didn't always go to plan.
I cry a lot in the car as it's the only time I get to myself (even if my lo is there - I just tell her that Mummy is a bit sad) and I pull myself together. I also tell my lo stories about mum all the time. Knowing how much my lo meant to mum, I know she'd want me to be the best mum I can be and I often have to remind myself of that if I feel a wave of grief.
My partner helped from a practical side, making sure I ate nutritious food, washing, helping clear the house etc. I also tried to focus in getting out the house everyday (we have a dog too), just made everyone feel better. But just take each day as it comes.
In dealing with the admin, it was a nightmare with a small one ready to kick off at the most awkward time, but most people I spoke to where super helpful and understanding. I tried to set myself small goals each day, but if I didn't get it done I tried to tell myself it didn't matter....be kind to yourself and remember at the moment you are holding everyone together so you need to look after yourself, don't be afraid to ask for help.
Does focussing on her gc help your Mum? There is also other support available from speaking to my midwife at the time, I didn't use it though.
It's super hard, but I was grateful for my lo as they gave me a reason to get up and continue. I would say it gets easier, but the grief is still there, just not as raw.
And remember you are doing a great job in such tragic circumstances and I'm sure your dad would be very proud.