My landlord forgot to put my children name in the lease, they need me to resigned the lease, what happens if I don't?

I renew my lease a couple of months ago, and now the landlord is calling me to stop by the office to re-signed the lease as they forgot to add the children in the lease, however due to my work schedule that matches exactly theirs I am unable to get there and sign the lease, the landlord was really rude and asking me all this personal questions about my work schedule and how come I work 6 days a week and why I can't come during my lunch and all of this, this is not the first time the landlord has been rude however this time it felt that it went over board, I have never been late in my rent or cause issues with them but they way they treat me is not acceptable. I want to know if i do not signed the lease what can happen? would that leave me in a month to month status?