"Interfere in" vs. "interfere with"

In the case of, for example, someone else's life, you can either interfere in or with. The former is critical of the fact that you meddled at all. The latter is critical of the results of your meddling.

OP's definition of interfere in is correct - it means to get involved (usually, in matters that others think don't concern you).

To interfere with means to disrupt. Wave patterns, for example, can interfere with each other. This means they are mutually disruptive. Whilst it's true that interfering in someone else's affairs may be disruptive, it needn't be. But if you interfere with their affairs, you're definitely having a bad influence.

There's also the idiomatic usage of a paedophile interfering with a victim, which normally refers specifically to touching a child's genitals. I think in this case the thing being disrupted is the child's (future) sexual identity, but most of us would prefer not to dwell on the exact meaning there.

I wouldn't say "in" and "with" are universally interchangeable in relation to "interfere", but I also don't think I would agree with your defined distinctions. The difference, at least for me, is the same as with the vagaries of prepositions in general.

As an American, here's how I would interpret these phrases:

"Interfere in someone's business" : to meddle in someone's personal life
"Interfere with someone's business" : to meddle in someone's proprietorship