Hi Tracey,
I don't think there is any way to really know about things like the dogs. It will be a rough road and will last a few months. Your mom will most likely need quite a bit of support. I do think it would be wise to take time off from work, if that is an option for you. At their age it will be hard on your mom to watch your dad. She will need as much support as she can get. But...you will need to take care of yourself too.
As for canceling a vacation...I guess it depends what long term means and whether or not you have anyone else to help them.
I hope tis helps a little bit. There are many unforeseens going into this. Everyone has their own journey. There are no absolutes!
Kathy