We are trying to be as reasonable as we can with this isue but our landlords seem to be being as unreasonable as posible.

Big project...the numbers don't seem unreasonable.

Many factors go into turn time and from a PM's perspective, it can be tough setting these expectations for our owners who may only have a single home that they used to self-manage and are expecting a maximum of 3 days (unreasonable).

She still feels its unreasonable to ask her to pay for the plumber.

Its another thing for it to go out.  68 does not seem like a completely unreasonable number.  

Seal off any entry points.I highly doubt it came with the tenant - this isn't a 1/8" cockroach.Also, don't consider the rent in this - you should have rented it broom-clean and free of infestation irregardless of what you charge compared to the market.If it got in in that one month, find out how, seal it up to prevent others, and kill the occupants (the rats, not your tenants).As far as the timing of their complaint vs. response- yes they are unreasonable, and now they can eat the cost of THEIR exterminator.

They seem to have unreasonable expectations and that usually clashes with landlords.

The tenants kind of don't have a choice, I could ask to receive the property empty, so nicely explaining to them that I'm going to screen them and then transfer the lease doesn't sound unreasonable to me.  

Am i being unreasonable?

Then state you are not willing to make the adjustments the program is requiring because they are unreasonable.