I am not sure where you are in Illinois, what the current market conditions are etc. What I would suggest is that you look for two things: first of for sale by owner, someone that is selling their home and is not using a real estate agent. I would look at the home and if it was something that my mother liked I would offer the owner a contract sale. This would be where you and your mother would give the owner substantial down payment and he would carry the mortgage at current rates plus a couple points to turn the house into an investment versus an asset. Understand that it may take you five or six or eight or 10 houses to find a situation where the owner will hold the contract but this will eliminate your problem of having to deal with agencies where you may or may not qualify.
The next opportunity would be to contact a real estate agent that works for short sales, foreclosures, and has listings of his/her own where the owners would be amiable to a contract sale. Since you have a substantial down payment you have funds to pay the realtors commission. The agent will also be able to check the MLS for homes that have been on the market for a long period of time. The sellers are more open to a contract sale the longer the houses on the market.
You may want to go to Zillow.com and investigate the homes in the neighborhood where your mother wants to live and on Zillow you can see what homes are for sale and how long they've been on the market. Find ones that you like, then contact the listing agent, see the properties, and then suggest a contract sale.
Be prepared to show a number of references to the seller to show that your mother pays her bills on time and the sale would be beneficial to both of you.
I've been in real estate industry since 1978 and have done many sales of this type.