A lot of pediatricians and psychologists put a lot weight on school evaluations. It’s tough because a lot of ADHD people do well in school with minimal hyperactivity, good grades, etc. They often miss inattentive type and also don’t account for the fact that some kids have a lot of self control when it comes to responding to authority or other rules.
I’d say that if you’re getting a lot of push back it may be worth seeking another opinion, though I know it would be hard to find since it seems like you’ve already have a rough time finding anyone to handle this. You could also ask the provider more about what more information they need in order to see the things you do. Have they given you parent rating forms? Have they done any of the various ADHD screening evaluations? There are lots of tools for providers out there but they don’t always use them. Either they’re not trained in them or the tools are expensive.
Keep doing what you’re doing. Write down a list of behaviors that you see at home. You can even look at the diagnostic criteria for ADHD and make notes and give examples for all the ones you see. You can find the criteria from the DSM-V here: Neurodevelopmental Disorders
Whatever happens, it may still take a while to get a diagnosis. There’s always a chance it isn’t ADHD, but as a parent if you know something is wrong it’s important to keep fighting and advocating. Good luck!