Is my mom right? Should I not let my child's record show he has ADHD and continue schooling with a IEP?

Okay. So I am a grown adult, in my 40s. But my parents (mom) instilled in my brain since I was a kid to never tell the doctor about family inherited or historical conditions, i.e., dementia, cancer, diabetes, ADHD, autism (unless severe), etc.

Now I have adopted kids, and the child seems to have ADHD and is about to start school. But my mom is now saying not to have the school mark him as ADHD and let him grow up without ADHD support.

For reference, we wanted our son to go to a private Catholic school, but now we are thinking of having him attend a public school that can support his ADHD with counseling and additional support. My parents want us to send him to private school and forget about his ADHD, saying that the private school will not kick him out for that and that they will treat him as a normal kid. He previously attended a Montessori school since he was 2. He was dismissed at age 4 because he could not sit still and would harass other kids by yelling (respectfully, as a 4-year-old that is learning to manage his emotions and self-regulate). The school wanted a one-on-one behavior therapist for him all day because he behaves, but maybe for an hour or two in the day, he would explode, and his behavior required additional support. We had him evaluated by the school district, and they concluded that he qualifies for ADHD support based on his behavior patterns at the Montessori daycare.

Now we are stuck. Should we send him to a public school and get the ADHD support, or should we just send him to a private school and have him with no support? Please provide me your thoughts or experiences of being diagnosed with ADHD. Do you prefer to have support or not?