2011 and 2015 Prius smart keys block each other from working?

Haven't posted here in several years. Finally decided to replace my 2004 (169k miles) with a used 2011 Prius Four, 74k miles. DH is leasing a 2015 Prius. We each carry smart keys for both cars at all times. With his fob in my purse, I cannot open or lock the door of the 2011 without hitting the fob button, nor can I start my car. The message comes up "no key detected." Another message says to touch the Start Button with the smart key, and that usually takes several tries to work. If I put his fob in the house my smart key works fine and I can open or lock the door as well as start up the car without touching the key.

The various threads I've seen mention a failing 12v battery, a faulty computer module, or dead fob batteries. The first thing I did after registering the car was replace the batteries in both fobs, so I know that's not the issue. Is it possible it's a fob programming issue? Is there some setting I can try myself before bringing it to the dealership and paying a ton of money? I never had this issue with the 2004 when I carried his 2012 or 2015 fob with me.

Edited to add: There is no conflict when he carries my key and uses his car. He can open/lock the doors and boot up just fine.

 

So I rephrased the search terms and found this thread. I see nothing has been done as of the last comment. I may call the dealership and ask if there's any news. If anyone has any suggestions let me know. Thanks.
two different key fobs in one prius | PriusChat