Greetings ShawnMicheal,
As long as your mother does not change her account..ie.
1. Switching to a new tier account.
2. Purchasing a new phone at a subsidized price from Verizon.
Your account will remain the same.
To renew your line, as you say, would require you to resign with Verizon for 2 more years. This is not necessary if your going to purchase your new device at full retail price. You will just be activating your new device on the line you have now. This does not require another contract with Verizon. Your account will continue to function as it has.
I would have a talk with your mom about this before you pay full price for a phone. If she decides she wants something else, and doesn't want to pay full price for it, the account will change if she gets a new device at the Verizon discounted price. Your unlimited account will be terminated.
If she wants something new, you could always get a phone off of E-bay or Craigslist to replace the one she has. Again, the account would not change because you do not have to renew with Verizon.