I'm so sorry to hear that, it is really hard.
Advice? Nothing guaranteed because as we all know intellectually when something really painful is happening, it hurts, but knowing it and having to deal with feeling it are two different beasts.
Take time not to be strong; you are important, your sadness, fear, anger, whatever you are feeling is a reaction to a situation you can't fix. So if you have a support network for you, use it, if not then make use of any provision, charities, or any services offered by your DF's care provider ( I've had contact with hospices and Macmillan, both were helpful with support for carers). It really is ok to say 'I can't deal with this right now' because things get very intense. You are NOT being selfish, you're being a grieving daughter. Totally human, totally normal.
I don't know how it might work for your situation but - outsourcing. The house might need cleaning and the washing done but paid help can free you up time, if you're visiting or caring for your dad while supporting your mum and your own family it soon feels like there aren't enough hours in the day. Or friends or family members pitching in, it can make a huge difference. Anything you can afford or Rota to reduce the stress of on going mundane tasks that threaten to overwhelm you is an investment in you, imo.
Do something frivolous with your mum. Letting your relationship contract to contain only supporter and supportee of your dad's illness can put real strain on things even though the only reason it's like that is love.
Ditto if you can face it at all, do something frivolous with your children.
If you can do a family thing involving your dad too then do that - a tree trimming party, whatever you can. It's not disloyal, it builds your reserves back up. Just laughing, I remember being almost limp with laughter in the hospice more than once - I needed it then, I cherish those memories now.
I thought my heart was crumbling with grief, I was watching my child die, but still we had the joy of those precious times. It makes you feel better, more connected and normal in the midst of chaos.
Accept that this is grief. That isn't meant to sound glib or to make it sound easy but actually making the decision to be as kind to yourself as if you were grieving the other way around and let yourself do it can be helpful. You are already grieving and that is painful and deep, it's ok to feel it's too much to bear sometimes so if standards slip a bit, is it the end of the world? Pressuring yourself to keep all the balls in the air, to make it seem ok and as if nothing has changed is too high an expectation. It has, you can all acknowledge it without it harming the time you have left.
What can your dad still do? What do you want to do with this time? Memory boxes, special events, anything like that. It's hard to feel celebratory but sometimes these are the best times. Just general closeness, time together or with the whole family. There's often a way to make things possible. Planning some of these events helped me, it may be anathema to others.
I'm sorry I have nothing better to offer but you have my absolute sympathy, I've walked similar paths and it's really difficult. Most of all I hope you can find a space to take care of yourself, being the main support for many people while you have your own heartbreak is real emotional heavy lifting, it's mentally exhausting at times and any space you can carve for yourself just to be can ease the pressure a bit. Talking here could help if you want to, as a space to just dump everything. Talking to a friend or not talking at all and having 20 minutes to stuff your head under a pillow in silence, but you aren't selfish, hold on to that whatever else you do