A seemingly ideal Bible Belt family man, is shaken to the core by a secret romance with a handsome young country and western singer that brings him his first real happiness, and the potential to destroy his life and the lives of everyone around him.

The overall plot seems very interesting and I see the conflict in there.

But you should try to shorten the logline, you do not need to say “destroy his life and the lives of everyone around him” you can simply say something like “destroy all he cares including himself” or simply “destroy his life” which is obviously not killing him so you don’t have to specify anything.

Also there is too much description, you don’t need to say “handsome young country and western singer” you can simply say “young sexy country singer”,

Also you don’t need to say “seemingly ideal” or you are precluding since beginning the first “shake” of the movie,
You have to show in the story that he was not an ideal bible man as he thought, not saying it in the logline.
Also go away with this happiness thing. Passion, love sell more and feels more interesting,
if you want to make him feel happiness you can make him meet a cancer patient a 9 years old boy or whatever. You want this man to feel attraction, passion, something that he did not feel from a long time it’s a goddamn young sexy woman!
Happiness can be a consequence of their relation, but you do not need to place it in the logline.
A logline has to hook, not show the entire story.

I would rewrite it like this.

“The life of an observant Bible Man is shaken as he falls in love with a dangerous young sexy country singer.”

You don’t need to say anything else about him destroying his own life or his family it is all already in the dangerous word you use to describe the woman.

Also I feel my version more appealing since the dangerous word can make you imagine a lot of things and is able to hook somebody reading the logline way more than your logline that was revealing too much while not making me curious.

Also I would change the bible man with a preacher. Nothing can create more internal conflict and a journey than destroying a man’s belief he is used to tell to thousands of people.