I think all the information given to you by the ladies is wonderful... what comes to mind for me are several things:
-animals are very psychic.. and protective... so he can also be protecting you.. but he may also be picking up at times on your dad's presence even if you aren't.
-He might still be traumatized over the loss.. you could go into a health food store and ask for some rescue remedy... dilute it in spring water.. you can put a few drops into his front paws in between where the claws meet the padding of the paw and rub it in gently with loving thoughts.. you can also do the same on the inside tip of his ear.. being careful not to let the drops go down into his ear.. also you can put some drops into his water... this is an excellent healing remedy for animals as well as humans in times of stress and emotional upheaval, etc.
You can pick up a small pamphlet or search online for Bach Flower Remedies. They will list the remedies with some emotional characteristics. If you scroll to the middle page of this link you will find what I am talking about.
making a tincture to give him out of the ones that appear to resonate what you are observing with him can help dramatically.. these are flower essences and are not harmful.
-lastly, I would encourage you to talk out loud to your dog picturing images of what you are speaking about as you would to help any one here at the boards, reassuring him of your love, and that you dad is ok... and that you would both heal from your grief in your own ways... and let him know you are tuned into him and will work to help balance him as well. I know you understand this....don't stay focused on the outer appearance... allow yourself to tune in...
keep us posted angel....gail