Vehicle stalling in rain

The starter see a fair amount of water when driving through even smaller puddles and getting splashed. It is pretty well sealed, but if saturatesd, I could see it shorting out. If a short was bad enough, it would have blown a fuse. If the car had enough water still in it or around it when she tried to start it, it actually grounded out into the water in every direction as it was the path of least resistance. This left the starter with very little power to start the car. The water dries up and the electrical crcuit follows the path of least resistance through a copper wire and everything is fine.
Very good analyzation that the starter is low and was the path that the electrons sought to follow. Since your daughter also had the good common sense to turn the key off and wait a while before trying to start it. All is well.
Whatever the path may have been it is fine now. I once had a headlight fill up with water and it made my car stall out. The buld grounded out to the reflective surface via water and burnt it up.
Take care and stay dry.

You must have an exposed wire under the car where the insulation has come off. You will have to look at the battery cables first, since they have been an issue, and check them for corrosion, any loss of insulkation that could cause a short, tight metal to metal contacts at electrical connections.
Since it is happening so easily in the rain/snow, I am betting that getting under the front with a flashlight will make finding it pretty easy. Most wiring is hung pretty high and if puddles and standing snow is causing shorts, the wire must be hanging low.

Be careful when doing so as sometimes you can trap water. Once show heats and metls it will freeze in any pocket you create. The good battery blankets and starter shields are equipp3ed for this. However the stater should not be acting like this.
Definately check the hot battery cable at both ends for a sure metal to metal firt as I can see it arcing in a wet situation if it is loose or if the ground is bad.
If you use a starter or battery blanket, keep a close eye on them, weekly, for corrosion buildup.
I think you may be looking for a battery cable that is loose or has the insulation worn off more than anything.