This must be an incredibly difficult situation for you and yours. It sounds as if your brother is quite adamant about not wanting to be a burden to anyone in
What remains to be seen is whether he will be inclined to modify these decisions once the more debilitating effects of lung cancer start to occur. He may feel very different in a few months; it is important to allow him to have his process with all of the information he is forced to integrate.
Hospice care is not just provided in the home. Maybe your brother would be more open to the hospice alternative if he knew that in some areas, there are hospitals or hospice guest houses that provide an alternative to hospice care in either his or his daughter's home.
To locate possible alternatives for your brother, you could do an Internet search for "hospice care," add the location in your search, and see what comes up. It might take some calling and researching, but maybe it will yield a solution that your brother would like.
Since he is a veteran, the other avenue to explore is what might be available to him through the Veterans Administration. You could initiate a search for information via the V.A. website or the National Hospice and Palliative Care Organization which has a specific page devoted to hospice care for veterans.
These ideas and suggestions are merely that: Ultimately, your brother will decide how and with whom he will live his final months. The only reason he shouldn't be the person to make the decision would be if he were deemed unfit to make it.
It is also possible that a good friend or a fellow veteran might convince your brother to choose an option more aligned with your family's wishes. If you or others in your family know of someone your brother really trusts or looks up to, you could appeal to that person for assistance. The disadvantage to this idea is that it could further alienate you from your brother if he ends up being unhappy with your actions.
Finally, if you disagree with your brother's decisions, it is appropriate to respectfully offer your opinions, and even to offer hospice or other housing alternatives.
However, if your brother remains firm in his course of action, your grieving process once your brother is gone is likely to be less difficult if you make an effort to respect his decision, honor his choices for the remainder of his life, and share a loving farewell.
his final months of life. It also sounds like he has made these decisions based on how he feels, both physically and emotionally, at least right now.