Vickie: Part of it is you need someone to support you during this time - as in an outlet to talk/cry. Been there - I had a friend who went walking with me a few times a week. Part of the conversation was about my parent who was dying but the rest was just of nonsense. It helped a lot and my weight went down and not up. It's hard when you have a parent who is sick and you have no control over the outcome or the things happening. Be kind to yourself as you help them.
For food: prep ahead and freeze especially if you are caregiving/visiting at the hospital, that way you know you have something good to come home to. You could also cut up a bunch of fresh veggies and store in the fridge that you can grab (my mom does this each weekend for the week ahead, sure it takes a bit of time, but she's got them ready whenever).
Stress eating for me is a hard one to overcome especially with loss, I turn to the sweets more than anything else. If you know your triggers and what you usually turn to maybe rid yourself of such. I have tried myself, it's harder than heck to do and sometimes you find you have hopped in your car to go get what you have been avoiding but sometimes you can make it through without these items.
Take care of yourself, let your dad know you love him and try the best that you can.