Putting the database (or any other qualifier like schema) inside the double-quotes is always wrong. Remember that a table name can legitimately contain a '.', so we would not be able to tell where the database name ended and the table name started.
I'm pretty sure that the solution is to use a table alias, i.e.
from "MYDB"."MYTABLE" AS "T1"
inner join "MYDB"."MYTABLE2" AS "T2" on "T1"."ID" = "T2"."ID"
Your solution would not work if the same table occurs more than once in the FROM clause (i.e. a self-join). So let's use aliases all the time. We'll obviously need to use aliases for other occurrences of the columns, in say the SELECT and WHERE clauses.