Thank you for clarifying. From what you've shared, it sounds like her father is enabling her. At her age, she should have a job and take care of herself even address her anxiety/depression by getting treatment.
If it is an option and you're willing/able to do so, ask him to join them once in a while for coffee. Even if she dislikes/hates you, on your end, you can still remain neutral/cordial with her. You're his wife and don't have anything to share with her except her father's time.
Perhaps he treats her this way out of guilt and is trying to compensate in some way. Yet, you're also a part of his family. You've mentioned that there had been arguments and that when she comes over he's reacting differently towards you. This may be a situation where outside help could be beneficial such as working with a couple's coach or marital therapist.
You must have feelings for him to want things to improve. He may have been unable to change his behavior so far and it does not mean that it has to remain this way.
On your end, try not to see her as a competition for his affection/attention even though from what you said, they spend a lot of time doing things together. Try to arrange things the two of you as a couple engage in. And, if she is to come over the house, perhaps you could also invite a friend or a couple/family friends to be there for dinner. That may break the ice a bit.
Something has to change for things to change. On his end, he'd have to be willing to examine how this is affecting not only you but the marriage. Both of you have to come up with a plan as to how to deal with this situation. It has been going on for too long. He may have become secretive because he feels guilty and does not want to upset you. Something to figure out is what makes this so upsetting to you and then address that. People can change with effort and as long as the two of you deal with this in a reasonable way, positive changes can happen.