This is a limitation of Steam Family Sharing caused by how it handles the data, specifically the fact it apparently only checks the first user in the sharing list when playing a shared game.
The program SFS-Select provides some functionality to help with this, and manual directions I'll share a part of below (mostly a copy/paste from a Reddit comment of mine):
Open /Steam/config/config.vdf
in a text editor. Preferably something other than Notepad unless you change the settings to handle Tab as a tab character and not spaces (if that's not the default, and is a setting? It's been a long time since I used Notepad). Personally I like Atom as I know it can fold the data, but other programmer's editors likely can do so too.
Find the key/title "AuthorizedDevice" and backup and then remove the contents, which will look something like the following if it's only the one person; otherwise you'll have to find out which user is which using something like SteamIDFinder or SteamDB's calculator so you can just remove that one.
"AuthorizedDevice"
{
"107311984"
{
"timeused" "1532591757"
"description" "Machine-Name"
"tokenid" "#"
}
}
When editing be careful of the curly braces ({, }) because if one is removed it will corrupt the file. And also the 2 tab characters between each "key" "value" pair -- Steam can consider the file corrupt even for this, but does not always do so.