I don't want to sound like a downer but I wouldn't count your eggs just yet. Money does strange things to families and since your mother didn't have a will there maybe some inside squabbling between you and your siblings. Things may seem all peace and quiet but when money gets involved people get greedy.
Just because you took care of your mother and paid for things while she was alive does not guarantee you a bigger portion in her estate. I would think the estate would have to be split evenly between your siblings no matter who cared for her.
My lawyer said that if I can produce receipts and cancelled checks proving I paid for my mother's care then I would be debtor on her estate and would be reimbursed for those expenses as well as her funeral costs.
If your mortgage is at a higher rate than the student loans, refinance it and still pay off the student loans.