Probably going to get downvoted to hell for this but that's not always true - the point about never trusting a dentist who doesn't let you back there. Some parents are horrible to have in the same room as the child because they project their own fears onto the kid.
I've had parents tell crying kids to 'shut up so the dentist can give you a needle'. It's not productive because the kid is already so worked up and if they weren't, then you've just created a bad environment. I tell parents that we don't use the N-word (needle) or the 4-letter S-word (shot) in the office because once kids hear that, it's a hard sell to even get them to open their mouths so I can take a look.
I do have rules of thumb (not absolutes) about when a parent can be back there, usually if I coach the parent first on letting me steer the appointment, what they can and can't tell their kid, and how they can help. Typically for me, kids under 4 can and should have their parents in the room because it make them feel more secure. At age 5+, kids can take direction from authority more but sometimes that means having the parent in the room is counterproductive.
If a kid is crying during a procedure, I always stop and ask them why. Kids are not the most communicable beings so sometimes being in uncomfortable situations, even without pain, can be enough to make them cry. Sometimes it's just nervousness and life goes on, sometimes it is genuine discomfort and then we add more numbing or even stop the appointment and refer out.
If you're a parent with a young kid who has never been to the dentist, let us do the talking. Don't explain what having fillings are like, or how anesthetic is applied. We do all that in kid-friendly ways. Don't call it a drill. Don't call it a needle or a shot. Don't use words with negative connotations like 'hurt' or 'pain'. Once you introduce those ideas into a kid's head, they grab it and run.
I don't call it a drill (technically it's not called that anyways but that's beside the point). I call it the 'tooth tickler' or 'whistle' because it only vibrates and makes a high-pitched sound if the kid is sufficiently sedated or numb. I don't call it a needle or shot, not even for adults, I say I'm going to make the tooth fall asleep. I don't say cavities, I say 'sugar bugs'.
What you should do is bring your kids to the dentist regularly and at an early age. Their first visit should be by age 1 or within 6 months of their first tooth coming through. What are we going to get done? Probably nothing productive, just a quick visit so the kid can see what we're all about - they ride the 'magic chair', play with the wind machine (our air/water dispenser), look at how small our mirrors are, they even get a toy at the end. Then we do it again in 6 months. Each time, I tell you what to expect next and how to improve your kid's oral health. You don't want your kid's first visit to be at age 4 for an emergency extraction of an abscessed tooth.
Some things are genetic, but cavities aren't. If you think it runs in the family because of genes, 99.999% that's probably not the case. What you inherited from your parents are not the genes for bad teeth but rather poor habits in terms of sugar/carbs and oral hygiene. Break the cycle, bring your kids in to have a good and healthy relationship with the dentist. We can coach you and your child with recommendations and information to set them up with good teeth for life.
Teeth haven't come in yet? Gently massage their gums with a Q-tip so they're used to having that kind of sensation daily. When they do come in, use the softest tooth brush and gentle massage the teeth twice a day, floss picks are great for fitting into small mouths. Use fluoride responsibly (don't believe the anti-fluoride campaigns) - grain of rice sized amount for kids <3, no more than pea-sized for ages 3-6. Look in their mouths for dark spots on teeth or anything else unusual. I've had some many parents bring their children in for massive caries in unrestorable teeth - when I point it out, the parent didn't even know it was there.
The least favorite part of my job is not treating rampant decay, or extracting broken teeth, or having someone accidentally nip my finger. It's seeing rampant decay in children. Kid's don't know what's best for them but parents should. Don't play it off as though nobody taught you - because I'm teaching you now.
I guess I'm getting side-tracked from that original comment and am making this into a rant so I'll end with this: I'm probably not the best dentist in the world but I try my best to help the people who come to me. It's a privilege to do so. I have training in dealing with kids and their parents so if I ask that you not disturb the appointment, it's probably because your behaviour, despite the good intentions, is not constructive to what we are trying to set out to accomplish that day. If I can't provide a good level of care for your child, I will refer them to a pediatric dentist who I've met and trust.