I can taste the difference between a house that has copper pipes and one with PEX pipes. Do you have some sort of water filtration system at the kitchen sink? Has it been properly maintained? There could be something wrong with the pipes going to either the kitchen or the bathroom, or something wrong with either of the faucets. Kids while perceptive can be really weird in what they prefer. Heck I even once had a kitchen faucet that was growing mold.

I can too I grew up drinking crappy water that had been poisoned by open pit mining. I don't think I ever drank clean, almost pure water until my 20s(unless I drank bottled water).

Pex is a god send. I used pex B in my home. High water pressure, easy install. The tools are a bit expensive, but well worth the savings. Also, pex won’t burst when frozen, but pvc/copper will. I learned that at my new home before I moved in, as my dad turned off the furnace in dead middle of winter. My toilet water was frozen in the bowl. My faucet in kitchen because a fountain.

Lead pipes by now would have so much calcium deposits, it’s not that dangerous unless you disturb them. But it’s still not good to have. Makes bad water pressure.

i like to think of it as kids have unbias senses, meaning there not likely to ignore things due to being "use to it"

Oh my God, outside water hose is the best! But as long as they are able to digest the bathroom water for now untill everything is fixed, the child can deal with the bathroom water. It's so much better than forcing toxic kitchen water on them.