If the passport is expired in less than 6 months one may not be allowed to enter USA, say if your parents comes after July 25 she may have to go back on the same day, have not heard about your case but it looked like it was linked to the one I heard before. I do NOT know if there will be still service for passport extension, these days a new passport is usually be issued. In any case you can try to apply for the extension, you have a good reason as your father get more time to stay. One problem though you have only one month time. Good luck!