There's not really enough information to provide guidance.
If I understand, you need 200k mortgage to be able keep the house.
One of the reasons you'd like to keep the house is because it has strong rental income potential? Where would you live when it's rented?
The alternative is to sell the house, take your share, and buy elsewhere with small / no mortgage?
Do you live in the house?
What's house worth? What's your income?
You mentioned joining sons to mortgage. It's possible, but they'd need to jointly own the house with you. This will greatly impact their own abilities to borrow for their own homes later. It will destroy their credit history if you go into arrears. They'd no longer be 1st time buyers in future.