Re: Hypothetically if your daycare provider.....
I guess in the end it depends how it is approached. If my DCP (I don't have one, I actually am one and a licensed prek-3 teacher) mentioned something to me, I took it to the Dr who then said they had no concerns and my DCP continued to tell me my DR was wrong it would rub me the wrong way.
It seems like you feel you know better than the Dr (in this case you very well might) but I can see that being off putting to the mom if she trusts her Dr.
I agree with whoever said mention things like "have you had his hearing checked?" I notice he doesn't respond when xyz, or he seems to not understand when I ask him whatever".
I would be defensive of someone trying to tell me something was wrong with my child instead of asking if I noticed certain things to, or just talking with me about things they notice.
It's all about how it's presented, but in the end if the mom doesn't want to do it, pushing her isn't going to make her do it, it will make her more defensive. So I would continue to mention things you notice every so often, but leave it there.
I would expect a DCP to present concerns, but not try to diagnose my kid. (not saying you are doing that, but presenting mom with a test could be interpreted that way)
Hi I'm Sara mommy to 4 little Mischief Makers