Lowrance is right . . . you can't change any of the terms of her contract (delete it or add to it) unless she contacts Verizon and agrees to relinquish her rights to you and you agree to assume liability for her line.   She left you the phone but did you also agree (privately of course) with her to pay her line until the contract end?   I ask this because technically SHE is responsible for that line, not you.   However, if part of the deal of accepting the phone was your promise to keep the line then keeping that line is honestly what you should do and I have a feeling you'll do the right thing regarding that.

To answer the second half of your question . . . you can start your own contract with the new phone of your choice and the two year contract price anytime you want.   But it sounds like you're trying to create a family plan by merging her remaining line with your new line and for that you will need her to contact Verizon as stated above.