How can I understand this sentence with "ce que ça ____"?

Question

^{(This is question #1 (of 3), about the same text that I quote in this question).}

Context: A social worker is speaking the following text¹. She is working with a case where two parents (with shared custody of their child) are in conflict with each other. The father is saying that the mother is constantly emotionally abusive towards him, whenever he picks up their child to visit him. The mother, in turn, has complaints about the father. The parents' conflict is putting a lot of stress on the child.

-J'ai une version d'un côté, j'ai une autre version de l'autre, chacun a sa vérité, c'est correct, mais leurs vérités sont trop à l'opposé.

Donc, moi, ce que ça m'apporterait de les mettre ensemble, c'est de voir: y a-t-il comme une espèce de juste milieu vers quoi on peut s'enligner pour ça.

Là, ce que cet enfant-là a besoin, c'est que ses parents réussissent à s'entendre un minimum.

Un minimum.

I'm having trouble understanding the bolded sentence.

DeepL's translation doesn't make perfect sense:

So, for me, what it would bring me to put them together is to see: is there a kind of middle ground towards which we can move for that.

My confusion might come from at least three places:

• I don't really understand what "m'apporterait" means.
• I'm not sure what "les mettre ensemble" means, though I have some guess about it.
• The "ce que" seems to be used in a construction that I'm unfamiliar with

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Here's my attempt at guessing a translation:

What would lead me [/help me] to bring them together, is to see: is there a kind of middle ground that we could move towards?

Here,

• my guess is that "m'apporter" (literally "bring me") means something like "lead me" or "help me"
• my guess is that "les mettre ensemble", word-for-word means "put them together", so here I guessed that it meant "put them [= "the two parents", or "the two opposing points of view"] together"

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But my translation ignores "ce que". It seems like my translation is using "ce qui" instead, (and doesn't include "ça") as if the sentence were instead:

Donc, moi, ce qui [∅] m'apporterait de les mettre ensemble, c'est de voir

If I try to understand the "ce que ["ça _____" clause]" construction, I get confused:

ce que [ça m'apporterait de les mettre ensemble], c'est de voir:

Here are some of my observations and guesses:

• Observation: Word-for-word, this translates to "What it leads me to bring them together, it's to see:". This doesn't makes sense to me in English. Somewhat similar sentences make sense (such as: "What it leads me to believe, is that the butler was the murderer!" or "What [∅] leads me to bring them together, is to see:"), but these somewhat similar sentences don't help me understand better the confusing sentence.
• Attempt at guessing: the part in between the [] that I quoted above can be translated. It says "It leads me to bring them together". So, if I try to add the "ce que", can I make sense of it? It makes me try to think of "ce que" as being a pronoun, replacing an object of a verb (maybe "s'apporter [qch]", but more likely "mettre ensemble [qch]"). That is, "It leads me to bring together [something]" --> "[What] it leads me to bring together". But "mettre ensemble" already has an object ("les"), so I'm doubtful that this idea (that "ce que" is an object of "mettre ensemble") is correct.

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Questions:

1. Can you give me a (fairly literal) translation for "Donc, moi, ce que ça m'apporterait de les mettre ensemble, c'est de voir: y a-t-il comme une espèce de juste milieu vers quoi on peut s'enligner pour ça."? That is, I'd like a fairly literal translation, so I can understand "m'apporterait" and "les mettre ensemble". Is the "les" in "les mettre ensemble" referring to the two parents, or instead the two conflicting viewpoints?

2. How can I understand "ce que ça ____ "? Was I correct in thinking that it really means "ce qui [∅] ____ "? If so, can you give me other example sentences using the same "ce que ça ___ " construction?

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^{1. From episode four of "Au coeur de la DPJ", at about 13 minutes 20 seconds into the episode.}

Answer 1

It seems the social worker has talked with both the parents, but separately. She heard both sides of a story, but it hasn't helped to reach an agreement. So what she would like to try now, is some kind of confrontation.

"les mettre ensemble" means to put them together, in the same room, around a table, and talk with both of them simultaneously, so they can make progress.

Given the context, "ce que ça m'apporterait" means "what it would bring to my understanding of this situation". But it is not quite an elegant choice of words (in french, I mean).

1. I cannot see any literal translation that stays close to the meaning of the sentence. The best I can find is :
   "So, to me, to put them together would help me see if there is a sort of common ground they could reach here."
2. You cannot simply switch from "ce que ça" to "ce qui" in this sentence. It would not be correct, and you would have to modify the sentence to keep its meaning. For example : Ce qui m'aiderait, c'est de les mettre ensemble pour voir si....

I am sorry if I did not give you the answers you were expecting. That's because the sentence you are struggling with, is a good example of poor style. I am sure one could find a translation that renders this, but I can't see how it would be possible with literal translation.