Many official metalink notes (like 280939.1 , 199272.1 , 399086.1 , etc) use DOP for Degree Of Parallelism , so it´s an "official" acronym, I guess...
Regarding the question : sure, parallel_adaptive_multi_user would be a VERY nice thing, ** IF ** the questioner had obeyed the rule, ONE database in ONE server, having two, no, nope : afaik the algorithm for parallel_adaptive_multi_user check number of session inside ONE database, it would not "know" nothing about the other db.... SO the answer is : manually, inside your application, CHECK the number of current parallel sessions and set DOP manually , like this :

IF number of active parallel slaves < your limit THEN
SELECT /*+ PARALLEL(x) ...
ELSE...

Probably will exist just a few situations (ie, system in idle, semi-idle, normal and busy states), SO will be possible to check for this with IFs, no need for dynamic SQL, I think.

Regards,

Chiappa