Is this true about the life of school teachers in the old west?

I think that's an exaggeration. Schoolteachers were expected to be models of morality for their students. A teacher who carried on an affair could lose her job. This meant they couldn't be seen with men, couldn't stay out too late at night, or at a bar, or smoking or drinking, etc. But just like politicians of today who trade on morality (like Mike Pence) they could get away with a lot if they just managed to keep it out of the news. The Victorian Era was actually a time of great immorality with adultery, drug abuse, prostitution, etc. at higher levels than even today. People just didn't talk about it as much.

Just recently I took a walking tour of the neighborhood of Pacific Heights in San Francisco, one of the wealthiest neighborhoods in the country, where homes routinely sell for tens of millions of dollars. The neighborhood grew up in the 1890s when big fortunes were being made in California. Right in the middle of the neighborhood is a boutique hotel that's one of the most expensive in the city (and in SF that's saying a LOT!) Originally it was built to house the mistresses of the millionaires who lived in the neighborhood.