Dad's girlfriend doesn’t like our close relationship?

Do they ever??

I don't see that there is anything that you can do. Your father is not diagnosed with any problems. If there should be a marriage the wife would most certainly win guardianship. Even were you to get POA you are far away, and the POA can be changed as simply as the girlfriend having him assign her after assigning you. Then she is once again in charge. You are also a good distance away? This makes assessment of what is going on almost impossible. If they are of a similar age, and she seems supportive of him, I would befriend her rather than anything else. You will get a lot father with honey for the bees than with adversarial relationship at a distance. She really is holding all the cards at this point.

If your dad has not been diagnosed there is nothing you can do long distance.

If he really has Alzheimer's you need to do some serious intervention or the girlfriend that is there everyday will be doing whatever she wants and you will have a tough time proving anything or getting your dad to talk against her.

Who has the POAs for your dad? If you do, use them to get him diagnosed so they can not be changed. If you don't, I recommend that you get them and get them ASAP.

Have you tried bringing your dad to your house for an extended visit to put some space in the relationship?

Bottom line is that he needs someone, so you step up or you will have to step away if he chooses her. You say he leans on her heavily, so immediate action is needed.

Good luck!