Hi, Jacob. You can say "get in trouble" and this phrasing would be particularly applicable to children or something children would say. Pete: If you eat a piece of cake before the party, you're going to get in trouble.
Sue: You're right. I'll eat a cookie instead. Dad won't notice if I eat just one.

It could be used in adult contexts, though it's informal and sounds a little juvenile.
Nancy: Are you going to the staff meeting this afternoon?
Armando: Yeah. I skipped last month's meeting and I don't want to get in more trouble than I already am.

To the best of my knowledge you can't say "get trouble" or "get (in) anger". With the idea of anger, you'd have to use the adjective "angry". As in: Bob's father got very angry when he learned that Bob had been stealing cigarettes from Walmart and selling them to other kids at school. It seems Bob is always causing trouble at home, too. The other day he was playing baseball in the living room and broke the window. That made his mother especially angry because she had told him to play outside.

You can also say "make trouble".
Principal: What are you kids doing here? Making trouble, I bet.

If in doubt, change it to 'problem(s)', a more neutral and official version of 'trouble'. That's the term I would prefer for writing about intergenerational frictions, by the way.

'to get in trouble' sounds odd to me.
I would say 'to get into trouble'.
It seems to roll off the tongue more easily.

Rachel, do you speak BE? Because in AE, I find get in trouble quite normal. And I'm pretty sure Amy speaks AE (correct me if I'm wrong, Amy). I would also definitely use an article, or put it in plural (problems, tensions between children and their fathers or between a child and his/her father).

Yes, I'm English.

I would say 'I am in trouble.'

But 'I'm going to get into trouble if I do that.'

Thanks a lot.

Can I "get into problems"?

And while we are on the subject: Can I only tell someone ABOUT my problems, or can I also say:

"I told her my problems."

I'd say "get in trouble" too (AE), though "get into trouble" certainly doesn't sound wrong. No, you can't "get into problems," though you can "land in a tight spot" or "end up in difficulties."

I would also probably rephrase your sentence as "This article is about father-son/daughter difficulties."

I wouldn't say "I told her my problems," but it doesn't sound wrong.

'to get in trouble' and 'to get into trouble' mean two different things in AE.

The first means to face someone in authority over something reproachable you have done, and is often followed by 'with + authority-person', e.g.
"I'll get in trouble with my Mom" or, "Are you in trouble with the law/with the police/with your probation officer/with Inland Revenue again?"

The second one is irrespective of consequences by any authority figure (though it doesn't preclude such). It means to get into a perilous situation with possible negative consequences: "If you take your small boat past the jetty in these gales, you could get into trouble," i.e., your boat could sink. ("...gales, you could get in trouble" would mean that as soon as you got back safely, the harbormaster will be after your license or impound your boat). "If you go into that honky-tonk, you're going to get into trouble" (you'll have a fistfight with some drunk--even if no police are there to arrest you and you get away, you'll still be beaten up).