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When your grandmother died (assuming she died after her husband and did not remarry) , ownership passed to your father and his brother. Each held an undivided 50% interest.
Upon your uncle's death (once again assuming he was unmarried at the time of his death), his 50% interest passed to his lineal descendants (your cousins), "per stirpes". This is a Latin term meaning 'according to descendance'.
The property ownership now would stand at - 50% your Dad; 25% cousin A; 25% cousin B. The expenses of the property should be borne according to these percentages.
When your father passes, his 50% interest will pass to you and your siblings "per stirpes". If you are the only child, you inherit the 50% interest.
If you truly feel that the property has no value, now or in the future, you should have your father quit-claim his interest in the property to your cousins. They would each then own a 50% interest and could decide among themselves how to pay the taxes.
BTW, in the line of descendance, only blood matters. Anyone other than sons or daughters never had or will have an interest.
No, I'm not a lawyer, but I was a Real Estate Trust Officer for a major bank and dealt with these situations every day.
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