Day of the week of an ambiguous date
Bash + GNU utilities, 97 96 93 85 80 76 73 58 56 51 bytes



(${d=date +%a -d$3-}$1-$2;$d$2-$1)|uniq|sed N\;cErr


Try it online!

5 bytes off thanks to user41805, who pointed out that I could use sed's c command instead of the final s command.

2 bytes off thanks to Nahuel Fouilleul. (Nahuel also helped by shaving 4 bytes off in an earlier version that has since been revamped.)

When I noticed that the separators can be any non-digit character, I changed the code to use spaces as the separator. 

This is called with a command like

checkdate 01 06 2020

The output is on stdout.  (There's spurious output on stderr.)