Can My Landlord Evict Me If I Simply Complain To Him About The Rules That Prohibit Kids From Playing Outside?

No. You don’t need to file a lawsuit to receive the protections provided by federal law. If you object to the landlord about apartment rules that unfairly discriminate against children, then the law prohibits him from retaliating against you in any manner. If he does so, his act of retaliation is a violation of law.