It is legal for grandmother and child to live in a one bedroom. If there is excessive noise, then you can complain to the landlord and they can bring an action against the tenant for violation of lease and seek eviction if an undesirable tenant.
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Dear White Plains Tenant:
A mother and child may live in a one bedroom apartment. A landlord cannot discriminate in renting residential housing because a tenant has a child or has children. 800 square feet (excluding the kitchen) provides a sufficient amount of dwelling space to accommodate an adult and a child.
You may express your concern to the Buildings Department of the City of White Plains:
Your legal issue seems to be the noise you experience living in an apartment beneath a child. If that is your issue you may complain to the landlord. Perhaps the tenant is required to carpet and did not do so.
The answer provided to you is in the nature of general information. The general proposition being that you should try to avoid a bad outcome if you can.