There are a thousand opinions on this, and the 'external/internal'
interpretation has never appealed to me as a speaker of American
English.
Students in most countries have to wear uniforms to school.
That sounds fine to me.
I have to tell her that her husband has been deceiving her.
That doesn't sound as good as "I must tell her ...", at least not in the reading intended, in my opinion.
This second one seems to me a special case of the usage of "must" --
something idiomatic, perhaps. It's a must that isn't really a
must. This "must" is the "take a mental note" "must", as in, "You
must come and visit us more often" or "I really must watch my language
more carefully around the children". Maybe we could even call
this the "ought-must" or the "toothless-must", since it lacks any real
force as an obligation.
In my experience and observation, Americans barely ever use the "must"
of obligation -- only the "ought-must" discussed above at times, and a
sort of "institutional rules" "must": "Employees must report to
work at 7 am" But we do use "logical" "must" extremely often --
the one that means "The only possible conclusion is that ...".
In all cases, "have to" can and does substitute for "must", at least in
ordinary conversation -- although much less so for "logical must".
CJ