OK, let's see if I've got this...
User can open database A and then can open database B in that order. BUT if the user opens B first, he then cannot open A.
Things I would check include whether in both cases, you have one or two instances of MSACCESS.EXE (it's correct name in this specific context). If you have two in one case and only one in the other, that is significant. However, since MSACCESS.EXE is supposed to be "pure" code, you should NOT need a second copy of the image file. So if the answer is "one copy" for BOTH cases, that is actually good.
Then, my usual issue is that when something won't open, can you "fix" it by closing the "B" instance, and in that case, does the "A" database open immediately?
I also am a fan of the debugging info sometimes found in the event logs. You need to find the Control Panel >> Administrative Tools >> Event Viewer - but on Win10, it depends on which theme you have chosen as to whether that path is available.
So anyway, trigger the failing sequence and note the exact time of the attempt that doesn't work. HINT: Either have a "clock gadget" on your desktop or look at the clock in the far right of the task bar. Since both of those clocks reflect the system time, you should be able to use the event viewer to see what happens at the times in question. If there is an error in the log, you have found valuable info. Usually, you only need to go at most one minute either way from the critical event to see what is happening. The down side of this is that you might not see anything. It COULD happen.
That would mean you have to run the Resource Manager in the background, run everything "normalized" (i.e. neither maximized nor minimized) in windows so you can also see the resources window. Then launch database B, let the resources settle, and launch database A. You might be able to see some resource dip towards zero.
Unless database B is "playing" with the registry or has opened something in exclusive mode that is shared by database A, I'm darned if I know what it could be... but that idea gives me one more experiment.
Open A, then B. OK, they are now both open. Can you switch active windows back to A and actually DO anything? If no, then the problem is that B is being opened in exclusive mode and has locked whatever it shares in common with A. Is there a chance that A and B share all or part of the same back-end?
