Will the former father-in-law or she be rewarded for my use of the prayer beads that her father gifted, knowing that I do not wish for them to receive any good from me after the divorce?

The Sunnah is to say Subhanallah with the hand, and that is better and brings greater reward. As for saying Subhanallah with prayer beads (masbahah), there is a difference of opinion among scholars regarding it. Disputes among Muslims should not reach the point of withholding reward, for forgiveness is closer to piety. It is desirable to forgive the oppressor so that the oppressed may attain Allah's reward and pleasure, for the matter is a transaction with Allah. And the one who guides to good receives a reward like the one who does it.