The rules pertaining to each hot tub holiday are made by the owners concerned. As a general rule, children are not allowed in a hot tub but this is discretionary and something that is agreed when booking.
Holidaymakers are often asked to sign a waiver form because use of hot tubs is not recommended for pregnant women or people with certain health conditions. You may not want your children to take any risks. Some people will always bend the rules but it is really a matter of common sense.
On the whole, hot tubs are safe to use in a sensible manner for healthy people.