Whether or not your landlord can terminate your lease due to the claim that your children are too noisy and there have been complaints about them would be determined upon the content of the presumed written lease that you have for the rental. As such, I recommend that you carefully read it in that its terms and conditions control the obligations owed by you to the landlord and vice versa.The lease may have a noise provision. Likewise, if you are on a month-to-month lease, under the law, the landlord can terminate your lease for just cause such as a noise issue that you are writing about.