Just so that I'm understanding right:
You own a "shack" that's worth $30k, has a $20k mortgage in your name, and you're up to date on these payments.
You own a number of cars that are paid cash, and that your kids use.
Your ex owns a house worth $180k, has a $110k mortgage in your name, and it's $9k behind on payments because your ex hasn't been paying.
Talk to a bankruptcy lawyer to confirm, but my belief:
If you do nothing and your ex either gets current with the mortgage by starting to make payments again, or decides to refinance the house in her own name, then she gets to stay, the bank is happy, and nothing happens to your credit.
If you do nothing, and your ex does nothing, eventually the lender on her house will foreclose and evict her. If the house sells for more than the mortgage (which is likely, someone will buy it for $130k or so, right?) then she gets evicted and the mortgage company will send her a check for however much money is leftover after paying the principal left on the mortgage. In this case, if the house sells in foreclosure for $130k, she gets kicked out and gets a $20k check, and you get a foreclosure on your credit history, and the bank is happy.
If you do nothing, and your ex sells the house, she gets to keep whatever is left after the sale. So if she's able to sell it for $160k, then she's moved out of the house and she gets a $50k check, you get nothing on your record, and the bank is happy.
Your job here is to convince her that she's going to be out of the house one way or another because she's not paying. She'll either move or get evicted, but that's her choice. It's up to her whether she wants to take whatever price the bank gets at auction for the house, or whether she wants to get a higher price by staging and advertising and listing it for sale the traditional way.
What you can be sure of:
The bank is getting paid.
She's either going to come up with enough money to get current on the mortgage, get a new mortgage herself, or move. She can't stay for free.
If she's leaving the house, she'll get more selling it "nice" than having the bank sell it as a foreclosure. If she likes money, she should sell it the traditional way.