Ich bleibe bei meiner Ansicht; vgl. die "halboffizielle" Übersetzung für die Vollstreckungsgegenklage:

Debtors are to assert objections that concern the claim itself as established by the judgment by filing a corresponding action with the court of first instance hearing the case....

Code of Civil Procedure (gesetze-im-internet.de)

I wonder if in your context you couldn't shorten the subject a bit by translating "tituliert" as legally enforceable.

.. objections. Objections that concern the legally enforceable claim itself and were already addressed in the proceedings are no longer eligible for consideration here.

Regarding "were already the subject of the proceedings" - that definite article worries me a bit. I would have thought the subject of the proceedings was maintenance for the child(ren).

About the past tense. I keep wanting to put "have already been" rather than were already. But I take it the proceedings are already over (or were over and then reopened)? It sounds a tiny bit strange to me the way it is, but I can't fix it. "Were already addressed in the main proceedings" or "were already addressed by the Court" would both sound fine to me, but alas, the German doesn't say either. Oh well, it might not bother anyone but me.