Does my mother have the right to be angry with me for seeking my legitimate right to my father's inheritance?

It is your legal and natural right to claim your share of your father's inheritance. No one is permitted to prevent you from this right which Allah Almighty has ordained for you, for Allah Almighty says: "For men is a share of what the parents and close relatives leave, and for women is a share of what the parents and close relatives leave, be it little or much - a share ordained." (An-Nisa:7).