Hello DrNortherner,
I'm sorry about your dad. Hugs to you.
I went through exactly the same thing with my mum after my dad died. I lived half a mile away from mum at the time, but even though I saw her or spoke to her on the phone several times a day, this still wasn't enough for her. In desperation I did some research and it seems that sudden widowhood quite literally blows a woman's world apart, and she isn't able just to pick up and carry on after a few months; it takes quite a long time for her to reach some sort of plateau from where she can start to build a new life.
Note that it's a new life, not a rebuilding of the old one, and this takes a while to come to terms with.
The key here is that, when she is ready (and this could take months - sorry, this sounds harsh, but it is best to be prepared) she will start to put out feelers and try to start again with her life. All you can do in the meantime is be supportive, and show her that you love her, but do not try to replace your dad as this will not help her in the long run. If she is saying that she cannot cope with everyday tasks - well, you live too far away to do these things for her, and in any case these are her tasks, not yours, so perhaps you could suggest ways in which she could get help to do them? Friends/neighbours/local support groups etc?
I know how grinding the "poor me" routine can be, and this does not diminish the love you have for your mum, but it is hard not to feel resentful sometimes (or more often!). This is normal.
Cruse Bereavement Care are very very helpful. www.cruse.org.uk. It may be too early for your mum to see them yet, but it might help you come to terms with things and to understand that you are not responsible for replacing your dad now that he's gone.
"How can I help her unerstand she can have a life without my Dad, even though of course we would prefer it if he was still here.
I always knew my dad did such alot for my mum, it's only after he has gone I am realiing just how much
I miss him so so much. The thought of this beig my mums future frighten me."
You probably can't help her understand that she can have a life without your Dad. She will come to this understanding in her own time, and Cruse could definitely help her with this.
It may get worse before it gets better. Again, sorry if this is not what you want to hear - I'm saying this coz I wish someone had said it to me 4 years ago! It will get better though. Please look after yourself, and don't allow yourself to feel that you must put your mum's needs before your own - you have lost your dad and you need support and love to allow you to grieve for him in your own way too.
I found that I was grieving for the loss of my parents as a unit too, as well as just for my dad. It took me a while to come to terms with, but time is a great healer.
Good luck and hugs and please post on here again if you need to x