1. Call Chicago area dealers who specialize in mid-century modern (google will help you find them) and see if they will buy outright or take consignments. I do not have any personal experience with any of them but I do know that as a general rule you need to know what you have and what it's worth before selling to a dealer; some are less than 100% honest. Just saying. Consignment is probably safer but be sure you get a signed contract stating terms.
2. Sell at a local auction. You might do really well or you might not--depends on who shows up and who wants what and how desperate they are to get it.
3. Find someone who will sell it for you on Ebay, but be aware that you will have to pay them a commission for it. Get terms spelled out very clearly, especially regarding what happens if there's damage in shipping.
4. Sell it yourself on ebay, craigslist, or at a tag/garage/estate sale. Research prices online.
Those are the main venues. I probably missed something. There's no stress-free way to do it, unfortunately.
oh, and no matter what you do---be upfront about everything. Undisclosed damage, repairs, inauthenticity--it can all come back to bit you in the butt later.
The John Toomey Gallery in Oak Park has about four high-end auctions a year in which they sell MCM items, exactly the type of items you listed. Each auction may have up to two hundred MCM lots, so it is exactly the forum you are looking for.
https://toomeyco.com/auctions/
.
I should have mentioned the Wright auction house, also in Chicago. They sell a lot of expensive MCM. If anything, it is even more high-end than Toomey, so if your mom has any early or rare pieces, you might want to check with them as well.
If you need any help, please contact us at – info@designaddict.com