Thirty-five years ago, my grandparent's deeded a camp with property to my father and my two aunts. During the 30 years, my aunts refused to help with the repairs and up-kept to the property, such as repairs roof, replacing stolen water well pumps, repairs due of theft and much more.
Ten years ago, my father deeded his part to my sister and I. Once I acquired ownership, I took responsibility because the camp had been abandoned and everything had been stolen out of the camp and destroyed. I refurbished having to drill another water well because the old well went dry, new hot-water heater, air-conditioner, all furnishings and furniture for kitchen, bathroom, bedrooms, all appliance's, TV, all new wiring, all new piping, ceiling fans, TV's, clearing land, fencing, security lights, garage doors, outside lighting, locked gate at entrance... ( everything you need to live... like walking into an empty house... thats how is was) and then I established residence, post-office box, phone, electricity in my name. In the meantime, my aunts are fully aware of this and still refuses to make any attempt to help. The only thing they have contributed is to pay $200.00 per year for their share of the taxes. Even when the Tropical-Storm "Rita" hit us in Texas and Louisiana, they never offered to help with the removal of the fallen trees that fell on the roof of the camp, repairing the roof and chimney and having the fallen trees removed to be able to drive and enter the property. They have never visited or cared about this property for 30 plus years and have repeatedly stated they are not going to send any money or help with any of the up- keep or repairs, quote:"we don't care if it falls to the ground, we are not helping and don't care what happens to the place." Now, after 30 plus years of neglect they are asking for keys to the property. My question is, do I have legal right to assume sole ownership of this property under the Adverse Possession Law?

Nope. As long as they pay the taxes, they are maintaining their ownership. If you sell the property they will share equally in it.

If you have saved all the receipts for improvements you have made to the property, you could make a case to be reimbursed for those improvements out of the proceeds of a sale then have the balance divided equally among the owners.

Adverse possession does not apply here. You CHOSE to make the improvements with the full knowledge that there were other owners of the property.