No. You err first of all in making the man a believer in the scenario. I never said he was a believer. You err in bringing God in the picture as far as 'will' goes. You err in assuming even if the man is a believer, God will save the other child. You don't know that. God doesn't always do that.How in the world could you get to that conclusion from this? It is a free will choice to not take God out of the equation.
Story. A long time ago, I was about where you are in my walk and I asked some guy basically the same question you asked about saving the kids. He answered that you save yourself because you can make more kids.
Now then, I could be that guy if I chose to. But I do not have to be that guy. I can choose to not be that guy. To understand that life (God) deals us impossible circumstances sometimes. God allows these things so we might become desperate and turn to Him, crying out for help.
Scripture tells us plainly that the Lord God is not slack in His promises. But it may seem like a spooky thing to put dire circumstances into the hands of an unseen entity, even many professing Christians. So many, including you would seem to lean towards taking the circumstances upon themselves and dealing with the circumstance on their own, and the way you describe your scenario one of the children will die. Scripture says, Ye have not because you ask not.
Hear wisdom Brother...Life is 10% what it deals you in the cards and 90% how you react to it. So if you do not seek first the Kingdom of God, you would be disallowing the Kingdom of God to intervene on your behalf in situations wherein you need some help.
If you want to experience divine intervention and witness the miraculous, then you have to get out of the boat. Remember in scripture when Peter got out of the boat and walked on water? That was only possible because he got out of the boat. Sure, he seen the big waves and started to sink, freaked out and said Lord save me!...and the Lord did save him. Peter asked, Peter received.
That's how this planet works Brother. He put us here with free will and He most certainly will not violate our free will. So if you choose to save one child on your own God will let you do that. Or you can simply pray Him and He will jump at the chance to bless you and save everyone involved. It's your choice. Your free will.
The point is, the man has to choose which child he will save. So which one is it? The boy or the girl? Which 'will' he choose.
If the man chooses the boy, is it his will that the girl drown? Of course not. But his will is not free. His will is pressured to make a choice. A choice that goes against what he would 'will' if his will were free. But his will isn't free.
Only God's will is free.