Lastly the ex is getting remarried and her and her spouse have a substantially large income so refinancing would logically not be an issue.
A high income isn't enough if the home is underwater - lenders won't loan more money than the home is worth, so she would have to come up with the difference between the new loan amount and the existing loan balances in cash at closing. Or convince the existing lenders to accept less than full payment, but of course that involves a "hit" against both your and her credit scores. Not as bad as a foreclosure, but definitely not as good as paying the loans off in full.
Even if her new husband has a lot of savings and can pay off the loans, he might not be willing to do that. I know in his shoes, or in hers, I'd be hesitant to start off a new relationship on such an unequal footing.
Two important bits of information would tell you a lot about the feasibility of a refi now: one, what is the current market value of the home, and two, what is the highest LTV (loan to value) ratio realistically available in the home-loan market today?
If the home is similar to many others in the neighborhood, you can figure out the fair market value yourself by looking at what similar homes have sold for in the last 6 months or so on realtor websites. In my area, they take all but one photo off the web when a house sells, so it's best to keep an eye on the market for a few months so you can save the realtor ads with all the photos while the house is still for sale, and then take note of the selling price later after it sells.
Be aware that the assessed value for property-tax purposes has no bearing on reality even when it's supposed to - I've been severely over- and underassessed at various times in different homes, even when the assessed value is supposed to equal fair market value (which isn't true in every state).
As far as LTV ratios go, a good place to start your research might be bankrate.com.
If your research shows the home is still underwater but is climbing in value, and you can verify that she has been making the payments on the mortgages and keeping the home insured, and that the property taxes are being paid, then pressuring her to refinance might actually have more downside than up. You do both need to think about how to handle that balloon payment, though.