However, the replacement property must remain an investment property—converting it into a primary residence too soon could trigger capital gains tax liability.

One of the other factors that kept me from pulling the trigger is that the city has never passed any real STR regulation.

The first factor to consider is Proposition 19, which will trigger a reassessment of property taxes if the home is transferred to either of your father-in-law’s daughters.

Although I wouldn't suggest this and you don't need to do this, most lenders have a due on sale clause and this could be triggered (altough low probability) when transferring title out of a borrowers name. 

Once you take an action, that can easily trigger tax consequences.

., mix STR with personal use or convert it to a primary residence), depreciation recapture is not triggered immediately but will apply when the property is sold.

However, this could trigger the due-on-sale clause if financed, so check with your lender.

If I would require some documentation from the city, would that trigger them to do the property lookup?

The last thing you want it to trigger income taxes from accidentally cashing out.  

Not ready to pull this trigger, but are we legally obligated to find a tenant or can we just tell them the offer has expired and that we are no longer seaking a tenant.