Some family dentists are VERY GOOD as children dentists'. Some are not!
It is usually at the discretion of the general local dentist to refer the child or treat personally.
Many factors come into play, such as the age and maturity of the child, the amount of work needed, and the general dentist’s own comfort level. Some 3 year olds are FINE seeing general family dentists, some 12 year olds ARE NOT.
It really depends...
To find a children dentist in your area click on the Children Dentist link