If it's the matrimonial home (you were married, not common law) then it's split 50/50 no matter who paid what.
If she is staying in the home, she pays you half the assessed value of the home. It's up to her where she gets the money.
If you have kids, the kids need a place to live, the cost of housing is a child expense, there is nothing remarkable about her using the CS to pay the mortgage. However if she at the edge budget-wise, she won't be able to continue once she has to pay you for half the house.
If you have moved out, you do not continue to pay for anything. You pay child support, that is all. If you continue to pay the mortgage, insurance, taxes, repairs, etc then that is just money out of your pocket that goes down the toilet, it will never be seen again.
If you pay for repairs now, you may get a better price when the home sells, but the value of the house will be split. You could seek to be reimbursed for your costs but that adds a lot of complications and arguing and legal bills as you figure it out and come to a settlement. The cheapest solution is the simplest, sell the house as-is and let the buy worry about repairs.
Of course every situation is different and if you spent $1000 cleaning it up and got $10,000 more in the sale then it is worth it. You have to judge what the repairs are worth. But 9 times out of 10 you won't get the full cost back from the sale.