Of course you will be angry. Your fathers place in your mind and in your family is the husband to your mother and just because your mother has died, they aren't divorced in your head and they won't ever be.
But your father has needs, and I don't mean sexual, he has a need for company and to feel good about himself and right now, he needs that to be another woman. He isn't trying to replace yuor mother, or forget her, or probably even move on, he simply needs to be cared for, and after the pain of losing your mother, he probably deserves from TLC, and not just from a family member.
If you can forgive him for having the need for human love, not just your love and know that she will never replace or be able to replace your mother, you won't lose a second parent too.
But your father has needs, and I don't mean sexual, he has a need for company and to feel good about himself and right now, he needs that to be another woman. He isn't trying to replace yuor mother, or forget her, or probably even move on, he simply needs to be cared for, and after the pain of losing your mother, he probably deserves from TLC, and not just from a family member.
If you can forgive him for having the need for human love, not just your love and know that she will never replace or be able to replace your mother, you won't lose a second parent too.