@Nicholas LIt appears that you are conflating costs and expensesCost is typically a one time event while expenses occur on a daily basis for line items associated with the operation of the property

One of the principal industry concerns about the vast power granted to the Consumer Financial Protection Bureau was that these powers were too insulated from review….The ruling sends a crystal-clear message to federal agencies that their powers are not unlimited…We would not be at this point today if government agencies were more prudent and consistent about staying within their statutory authorities, grounding their rulemakings in empirical facts, and heeding appropriate procedural safeguards…Instead, too frequently, our regulators appear to be chasing headlines and short-term political wins.”National Association of Homebuilders - “Today’s Supreme Court ruling is an important step forward to advance meaningful regulatory reform because it means that federal agencies can no longer continuously change the law – and the intent of Congress – by implementing their own interpretation of statutes as long as the interpretation is viewed as being ‘reasonable.’

Quote from @Dylan Ritch: Your problem appears to be analysis paralysis.

Do they appear well connected online and in real life?

The husband states "we will pay 1600 but these other two will have to come up with the rest cause I ain't paying the rest" and appeared to be irritated .

It appears you are planning to Proceed with caution which would be my advice.  

Often old houses have some rooms which are not flat even if they appear to be so to the eye.Also, when you are spending money, you want to make the biggest difference for the cost.

So I strive towards using Lodgify which is a standalone solution that hosts creating a web front, connectivity PMS Channel manager with seamless integration with air airbnb and booking.com. although the platform is very useful we are now seeking towards expanding to a new platform that can onboard us with more rental platforms، based on my research I found a channel manager by a company called Rategain, unfortunately we cannot integrate it seamlessly so the solution would've been to use automation software (Zapier) that can bridge both platforms.

Then hover over services, a drop down box will appear and click select short term rentals.

Every system you try will have flaws, or you may salivate over a feature that appears in other software.Some familiar names are mentioned frequently: Stessa, Apartments.com, RentRedi, TenantCloud, Innago, RentManager, Avail, Rentec Direct, Doorloop, etc.I recommend conducting thorough research on each app online to understand their offerings, pricing, etc.