The chances of you finding a lender to refinance your second lien after modifying the first mortgage would be pretty much non-existent due to the credit impact of the first mortgage reporting that it has been modified, which means that it is not being paid under the terms of the original Note.
With the competitive market it won’t be difficult for one to find a lender or a company who would refinance for the second mortgage but besides that make sure to go with the interest rates. As in your case if you would be able to find a lender who agrees to refinance for your second mortgage then surely the rate of interest would be quite high. So if you are able to manage that then quite feasible, else stick around for quick cash and get things done accordingly.
Good reason to refinance on 2nd mortgage is,if you are presently paying a high interest rate.If the mortgage rates are low,you can refinance it.