Yes, you do need to pay rent for the time that you are there, unless the landlord agrees otherwise.
I disagree that 2 adults and a child cannot live in a one bedroom apartment. There is a general rule that allows for two people per bedroom, plus one additional person. If you have a one bedroom unit, then three people can live there. However, if you have a lease, it might have some restrictions.
It is possible that your landlord's eviction is discriminatory.
You should contact a landlord tenant attorney in your area for a consultation.
Yes, you still need to pay rent for the entire 60 day period. If you wish to terminate the tenancy earlier, you can serve the landlord with a 30 day notice of termination. If you do not pay rent, the landlord can serve you with a 3 day notice to pay rent or quit, and/or deduct unpaid rent from your security deposit.
The landlord cannot discriminate against families with young children. If you wish to challenge the eviction, you're going to need a tenant attorney to represent you.
Frank W. Chen has been licensed to practice law in California since 1988. The information presented here is general in nature and is not intended, nor should be construed, as legal advice for a particular case. This Avvo.com posting does not create any attorney-client relationship with the author. For specific advice about your particular situation, please consult with your own attorney.