An apartment can make rules against children only if there is some type of potential danger to the children and if the rule is not too broad. Generally, rules that prohibit riding bicycles, riding scooters and skateboards, or playing with toy are illegal.
If an apartment has a rule which does not allow children to play outside during the day because other tenants are sleeping, this rule is illegal. The law states that it is a common known fact that children make noise and that adults have to put up with the noise children make as long as the children are not being unreasonably loud. Sometimes, children can be too loud. For example, if children are running around an apartment complex at midnight playing hide and go seek and screaming, then it would be reasonable to ask them to be quiet. However, rules which generally state that children must be quiet during the daylight hours are illegal.
Maybe. If the children are accused of being too noisy during normal hours, then the attempted eviction is probably illegal. However, if the children decide to play music extremely loud at 2 a.m., then this might justify the eviction.