@LettuceP I have almost exactly the same scenario. My DD has just been diagnosed with ASD at 3.5 because after she started preschool in January they picked up that she wasn't behaving in a way they would expect for a child her age (various reasons). Not classically, stereotypically 'autistic' though.
I know my DD better than anyone else I have spent almost every single day with her for 3.5 years (I'm a sahm). I didn't know she had autism though. I knew she had a few quirks, and that she found socialising with her peers hard. I thought (because so many arseholes said it) it was because she'd been at home with me and I'd somehow made her feel uncomfortable with groups of children by not mixing her as much as I could have.
Nope, she has ASD. I could've taken her to every single toddler group going and she'd still have it. I didn't spot it, and why would I? She is a 'normal' 3.5 year old to me, because she's all I know! My other child is younger.
OP this sort of tripe is usually spouted by people trying to justify doing something that goes against guidelines or common sense. Usually 'huns' to gather round to chorus 'mum knows best'. Also anti vaxxers seem to utter it frequently.
Mums do know, I believe when something isn't quite right, mostly. But mums do not know everything and do well to listen to medical advice etc.