advice on tenant not paying new rent increase

[Xiao C.]

Hi,

I'm new here and also green when it comes to rental properties in California. Currently, my family ran into some issues with the tenant and I would love to get some feedbacks.

The background. We have a single family home rented out for 2+years to a tenant and in the beginning of July, we'd hand delivered a letter to one of the tenants notifying them of a $50 rent increase effective this month (September). When we went to collect rent over the labor day weekend, they've only pay the old rent but not the new increased rent, which we believe is intentional on their part. We've also send out a text message to 2 of the tenants (previous communications were made via SMS) to remind them and to let us know when we can get the remaining balance of rent. They've never replied back to us. 

What are our options? 3 day notice to pay or quit? 60 days notice to terminate lease? If I do the 60 day notice, do I ignore the rent increase notification given to them almost 2 months ago? If I do the 3 day notice to pay or quit and they pay the owed balance, can I end their lease in a few months from now? They are not very good tenants, so I would prefer to end their lease sooner or later.

Right now, I am composing a letter to send them demanding payment for the remaining balance. Am I allow to add a late fee payment on top of the remaining balance since they did not pay in full and the grace period is over for late rent? 

Any advice is appreciated. Thank you very much and sorry for the long post.