First, a methodological note on the original post:
You started with the presumption that this practice is wrong and are looking to magisterial texts for support in this. I think this is not the best way to go about it. You assume from the outset that what you think is what the Church teaches. It would be better to say, well, I think this is wrong, but what is Church teaching on the matter? Are you seeking truth, or are you seeking to be confirmed in your opinions, and to show others that they are wrong? If you presumed your own view, it might be easy to find a magisterial document which seems to support your position, but wouldn’t in actuality if you hadn’t come to it with that particular lens.
Leaving aside the question of interfaith prayer being confusing, I want to tackle the issue of whether it matters whether everybody understands God correctly, and is therefore praying to the true God. Many Christians have an inadequate understanding of the Trinity (I was taught modalism, quite innocently, in CCD).
One quote I found in a magisterial document, though the authority of this particular statement is not very high, is from John Paul II in Redemptoris Missio 29:
"Excluding any mistaken interpretation, the interreligious meeting held in Assisi was meant to confirm my conviction that “every authentic prayer is prompted by the Holy Spirit, who is mysteriously present in every human heart.”
Whatever one thinks of Assisi, the truth that John Paul was trying to get across is quite valid. If all creation is groaning, does that not include the peoples of the earth, when they cry out for redemption?
Do prayers go unanswered if not directed correctly? All true prayer is directed to the True God, whether or not the person in question understands it, and all true prayer is the mysterious prompting of the Holy Spirit. However, Christian prayer is not the same as other prayers. The Christian’s relationship to God is fundamentally different. And thus, to pray publicly in common with others tends to discount the idea that the Christian access to God in Jesus through the Holy Spirit is fundamentally different than other experiences of prayer, because to outward appearances, they would seem the same.
For these last reasons, then, I don’t think interfaith prayer is an advisable practice. I think it would be truer to the situation if, when peoples of different religions encouter each other, the separate groups prayed separately, and then went on together to other things that they could rightly work together in, to be able to live their own identity fully. What does it help, to pray together, which praying separately would not accomplish, except to breed misunderstanding?.
But you probably won’t find magisterial documents on the matter, or else John Paul II probably wouldn’t have held the Assisi meetings at all. After all, he was surrounded by smart people, and even those who disagreed with him did not think it a matter of magisterial teaching, but rather of prudential practice. Still, even if it is not objectively wrong, it should not be entered into lightly, and it would make sense for groups doing this to consult their bishop on the matter.