This involves some fairly complicated legal rules from two different states, but the simple answer is that your father's wife's money probably will not affect his eligibility for Medicaid.
When your father (or you, on his behalf) applies for Medicaid coverage in Nevada, in deciding his eligibility the Medicaid program will consider all income and assets available to him. Because his wife's money came to her before their marriage and was always kept separate, the laws of Illinois probably -- here's where it can start to get a little complicated -- state that the money belongs solely to her, and not jointly to her and your father. If the money does not belong to your father under the law of Illinois, then it is not available to him in Nevada and the Nevada Medicaid program will not consider it part of his assets in deciding his eligibility.
You should be aware, however, that the Medicaid program can consider the value of the room and board you furnish your father as part of his regular "income." So, be careful not to overstate its value on your father's Medicaid application. If, for example, he receives Social Security benefits, is covered by Medicare, and has no rent or food bills to pay, Medicaid might find that he is not eligible for Medicaid because the total value of his "income" puts him over the Medicaid eligibility limit.
Another factor that may affect his eligibility is the amount of his regular Medical bills: high regular medical bills that are not paid by Medicare means a greater likelihood that he would qualify for Medicaid.