I’m sorry to butt in here with my controversial self (I guess I’ll get more red dots, dunno) but…
this is a CHILD with a severely compromised life. If she is TRULY choosing this baptism, it means she has the cognitive ability to accept Jesus and love him with her entire heart and in this camp she is being taught that full immersion, a conscious choice, is necessary. I find it impossible to believe God would fault her in any way. This fight belongs between you and your wife: you have a serious problem here.
People who choose full immersion baptism in any church where Jesus is greatly loved and His words are acknowledged as truth, where He is savior and king, do so because they have come to believe it is required. I was so baptized 20 years ago in an evangelical congregation! Does that make me a candidate for HELL? I don’t THINK so. I know my confessor certainly didn’t think so when I did a full life review with him two years ago. I did it out of obedience and complete trust and love for Jesus. We, Catholics, re-confirm our baptismal vows every single year. While we don’t get physically watered (so to speak), we re-affirm the vows made FOR US by our godparents while we were infants.
I think too much legalism creates fear and terror. I think God honors the hearts of those who love Him so long as their choices don’t revolve around flying into buildings and blowing themselves up along with innocent people. I think this child is innocent and, if she is truly making this step FROM FREE WILL and not from indoctrination or ANY PRESSURE WHATEVER from the people who run this camp, is totally free from any error.
You and your wife need a series of sit-downs. You can’t raise a child in an atmosphere of division in religious tradition and dogma. Something’s gotta give here. So now: awaiting the axe, or whatever else will befall me. (sigh)