My goodness poor you , what a situation. You must feel you are being pulled in all directions.
Personally I think you should see your folks as soon as poss. I think if something bad happens to your dad and your not there you will feel real bad.It is a toughy as you have a lot of commitments to your animals. It sounds like you have a lot of support from your DH and kids, so im sure you will come to the right decision.
Hope all goes well with your dad. Sending hugs.
