I agree 99% with Barbara Kate Repa's answer.
As far as I am aware, a Line of Credit which is in essence an ability to borrow money cannot be considered an Asset for Medicaid purposes. A Lump Sum payment AND a monthly payment not consumed which remains in the Senior's bank account CAN INDEED affect Medicaid eligibility.
The use of POAs with Reverse Mortgages is a very complex issue. HUD/FHA wants to be certain that a POA is used in a manner which is entirely in the Senior Citizen's best interest.
Generally, it must be reasonable to assume that the Senior was competent when the POA was issued. Furthermore, if the Senior isn't competent at this point, information must be provided that shows when that incompetence began. Usually a Physician's Letter is used for this purpose.
POAs must be durable, which means written in a way that allows their use when a Senior is no longer competent, and they must have the correct language that allows the POA holder to take out a mortgage.
The Pitfall here is that years ago, POAs were written very generally, such as "I give Person X authorization to do everything". State Laws and Rulings now require POAs to be much more detailed about what the holder can and cannot do.
Since your mother-in-law isn't competent at this point, should your POA be found to be not clear enough, there is nothing that you could do.
You would face another challenge because generally HUD/FHA does not allow Reverse Mortgages to be done if a home is suddenly put into a Senior's name. In this case, you might be able to get an exception, but there aren't any guarantees.
Putting the home INTO her name would not be an issue, as the "Grantee" or receiving party isn't an issue in this type of DEED. The question would be whether doing so would actually do any good.
You have a very difficult situation here. You did not indicate why your mother-in-law doesn't qualify for Medicaid at this point. It is certainly the case that were she to be moved to a facility in the future where Medicaid funds would be used to pay for her care, that Assets from the house would be used to pay for that care.
A key question would be if proper in-home care could be arranged, what funds would be forthcoming were a Reverse Mortgage to be put into place, and how long would such funds pay for the level of care she needs to stay at home.