@carrieann1223,
He is STILL on his hunting trip? If so, I think you are within your rights to go pick up the kids and keep them until his return. The girlfriend is not their guardian. She has no rights to authorize medical treatment if there is an emergency. She is an unrelated individual whom your husband has handed your kids over to.
Of course, I am not a lawyer. So you might want to run the above advice past one first. But if it were me and I had an ex-wife running off on a long vacation and she left my kids with her boyfriend, I would have picked them up as soon as I was aware of it.
As for the homework thing, she has NO right to tell you that she is taking the daughter home early from your house in order to do homework. Of course, you need to see that she does the homework while she is with you, but she has no right to ever pick your kids up for any reason without his presence. (You can of course ALLOW her to pick them up without his presence, but you are under no obligation to turn your kids over to anyone other than him, as far as my limited legal knowledge is concerned.)
All of the above assumes you are not leaving out any important information.