What should I do regarding my brother's request to save pictures of my deceased mother on the computer, given my belief in the impermissibility of photography, and am I obligated to erase the pictures I have with my mother on my phone?

If you are inclined to believe that photography is forbidden, then act upon that for yourself, and do not object to those who differ with you, because the disagreement regarding the permissibility of photography is valid. Accordingly, you may give your brother your mother's phone with her pictures on it, and you may remain silent about your father keeping your pictures. If you do speak to him about it, let it be with respect.