It sounds like it's still your mom's, so I don't know how much, if any, decision making power or influence you have.

I was wondering how much influence the owners have in the transaction

The people who did this are my parents and I am doing everything I can to minimize their influence in my life, but it is difficult, especially as an only child.

In most states they heavily influence or control the state real estate agencies.

If asked, that's a different matter, now your making representations that they may make a decision on that influences the accepting an offer and with a government entity or a bank, that can be an issue. :)

This is due to the influence of unfavorable factors on housing and mortgage markets.

Because of this, the only people that'll be in Pittsburgh are older generations (who already have homes or if they don't, won't be looking for one) and rural Pennsylvanias who treat Pittsburgh as their Philly or NYC with less "liberal influence". 

Over the last several months Sedona residents, who feel their town has been overtaken by STRs, have been outspoken in their opposition...and have gotten the attention of the governor:https://www.azcentral.com/story/news/politics/arizona/2019/08/22/arizona-lawmakers-revisit-short-term-rental-law-governor-ducey-airbnb/2089887001/https://www.azcentral.com/story/news/local/arizona/2019/07/25/sedona-residents-challenge-rep-bob-thorpe-over-vacation-rentals/1811064001/While any legislative crackdowns seem to be directed toward corporate "party houses," individual STR owners in Sedona, especially, could get caught in the crossfire.Cities in Metro Phoenix like Scottsdale, on the other hand, are more diverse and dispersed in terms of STR locations, so we have not seen the high-volume backlash by residents that Sedona has experienced.When you are deciding where to invest, check local news sites for stories on vacation rental legislation and policies.

What influences guided you? 

Poor academic research that hopefully will not influence policy much.