I'm Lucy, and I'd be happy to answer your questions today.
The only way to get your partner's name off the mobile home is for your partner to sign a deed transferring full ownership to you. If she won't do that, you're allowed to go to court and file what is called a Petition for Partition - but you'll be required to pay half the value of the equity home, because you are legally equal owners with equal rights to the value of the property. You'd only be able to avoid paying half the equity if you have something in writing that says otherwise, signed by both of you. I mention this because you may be able to work out a lesser payment to your former partner and avoid going to court. When there's nothing in writing, you're considered to be 50/50 owners, and you each are legally entitled to half the equity when one of you wants to buy the other out or if you were to instead sell to a third party.
Lot rent is the same. You're only entitled to reimbursement for half the lot rent if you had some sort of agreement that your partner would help you pay it after moving out. Otherwise, your partner could come back and say you owe half the rent that would've been obtained from renting out the mobile home rather than you living in it by yourself (since, as half owner, your former partner had a right to live there or to rent it out). So that might not be the best option for you - you could sue for lot rent and wind up paying her more than you're asking for.
If you have any questions or concerns about my response, please reply WITHOUT RATING. It's important that you are 100% satisfied with my courtesy and professionalism. Otherwise, please rate my service positively so I am paid for the time I spend answering questions. If you are on a mobile device, you may need to scroll to the right. There is no charge for follow-up questions. Thank you.