There has been a long-term tenant in place who just vacated and the property is outdated and needs to be rehabbed.

The vacation rental market hasn't suddenly dried up.

Or short term vacation rental?  

He also sent us a text stating that they will vacate the property at the end of their lease and to not schedule any viewings.We replied that the Civil Code allows us to enter (citing that we are entering during business hours, giving almost 48 hour notice and the reason as to why they are entering).

I’d like to give a proposed notice to vacate, and if payment is not received by X days, follow through with an actual notice to vacate.

Over the last several years, all of the talk has been "how much cashflow can I make with my vacation rental investment?" 

@Marysue ConnellyI'm not a lawyer and this isn't legal advice.Currently, if you want to discontinue a lease that is expiring, you simply need to provide a written notice to vacate to the tenant with the appropriate notice period - our lease agreement states 60 days unless a lease is month-to-month, Colorado law typically only requires 30 days notice.

I also recommend giving him the notice to vacate, he is not willing to acknowledge rent increase or sign a lease. 

My wife and I are looking to invest in existing or project-stage vacation rentals in Mexico / the Caribbean.

It's like they got their golden ticket so now it is time to go live and relax in a small vacation town.