Oh hatsy - I really feel for you. I was in the same position a couple of months ago and it's so madly unfair - also had the same problem with running! (Don't suppose you have a random relative in the medical profession who keeps calling you to find out what drugs the hospital have given your mum on any given date, do you?)
For myself, I was lucky(ish) in that I had relatives and friends who had been in my position before and I could vent to - I found a lot of people expected me to be solemn and reverent all the time which really isn't me; those who had gone through it were more able to have a laugh at the funny bits, if that makes sense. This thread is great for that too. I could be as amused, resentful or whatever as I liked and I knew people would get it.
The unfairness really struck me too - I knew I would probably throttle anyone who said "And did she smoke?" - Mum was pretty healthy, never smoked, and her non-high-risk status was part of what meant her diagnosis was too late ('must be a chest infection as you've never smoked'). I still get the rage at lots of the cancer awareness things 'don't smoke and eat lots of vegetables and you can help BEAT CANCER!!' - well, yeah. Cancer doesn't look at a diet sheet and say 'well, she's eaten an orange this morning, so I'll move on to the chain smoker down the road'. I sent a rather grumpy email to our HR team after they'd started a 'BEAT CANCER!' campaign along these lines; to date I still have a job...
The best advice I got at this stage, ironically from someone who has no kids of their own, was to keep as much to a normal routine for my daughter as possible. Knowing I had to get her from nursery in the afternoons, make sure her clothes were ready in the morning, make sure I gave her a bath and put her to bed, really helped - I was on auto-pilot but it gave me something seperate to do and I could switch off my 'hospice head' for that time. Do you have DCs?
As for drinking and eating too much - join the club! I figured at that time that this was a very temporary time in my life and so long as I didn't go completely overboard it was fine.
I would take it one step at a time at this stage. I found organising the funeral much more straightforward than I thought it would be, and it was good that Dad and I had something to do together. Didn't feel I could manage a eulogy myself, but it was nice to contribute to it.