My response - “if you stomp in a puddle when there is someone else close by, the water might splash them, and they might not like it. Please be careful when you are splashing”
His response - “Hey “child’s name”! Not. Cool. You just splashed me. That’s not ok. Don’t do that.
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Imagine you have a meter of "Tolerance". At 100%, you are totally calm and at peace. At 0% you're losing your shit and freaking out.
Your comment reads as someone at 90% tolerance or more.
His comment reads like someone at 50% tolerance or a bit less.
I would expect someones tolerance level to drop proportionally to the amount of times they have already told the child off, how severe they perceive the misbehaviour as being, how tired that person is at that point in time, how much stress that person is under at that moment, and any number of other issues that might drop someones tolerance levels by a few percentage points.
Him being further down the scale than you doesn't mean there is anything wrong with him. There might similarly be times where your tolerance level is lower than his. That doesn't make you worse than him.
When you introduced him to your kids, and they only spent an hour or two together, did he sound more like his tolerance level was higher? Does he usually speak to them more like your first comment? Or does he always sound like his tolerance level is very low, regardless of circumstance? Is he always short with them, or only this time, now, when he's spent days with them, unable to leave?
If he always sounds like he's low on the meter, then yeah, that's a problem you need to either resolve by having some conversations about it, or find another partner. It might be that he's genuinely bad with children. It could be that the only role model he had for talking to children was his own father, who may or may not have been a good one to begin with. Certainly if he grew up in the 80-90s then attitudes on how to parent children have moved on, and it's not like he's going to have kept up with modern schools of thought on behaviour management. Why would he? He also probably doesn't read websites like this full of tips and tricks on how to deal with children.
However if he's only sounding like he's low on the meter now and he's usually higher, then simply have a chat with him about it. "I get the feeling that the kids are tiring you out and I'm sorry that it's not as perfect as we wanted it to be. Let me deal with everything to do with them for a bit, and you just chill out and get your strength back."
Either way, absolutely nothing is going to change unless you have a conversation. His meter will continue to drop if you don't do something about it.