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Norbert,

That does seem to confirm the cause of the problem.  You still need to
resolve this.  You are, after all, responsible for the outdoor cat and there
will come a time when you need to get hold of him for a vetinary visit, even
if it's only for boosters.  He should also be protected from fleas, ticks
and worms.  Somehow,  you need to encourage him to come indoors; he needs
his own territory indoors, which must be categorically upheld by all the
family.  When indoors, he should have all the fuss and play stimulation he
needs.  None of this will be easy, but you owe him some inclusion in the
family home - almost whether he wants it or not.  Otherwise, you will end up
with a semi-feral cat.

The only other option I can see would be capturing him and taking him to
your local cat rescue for rehoming.  He will need to be rehomed somewhere
with a garden (he will have come to enjoy exploring outside), and where he
is either the dominant cat, or the only cat.  Even if you're not sure about
rehoming him, consider talking to cat rescue as they can probably give you
some very good advice.

I do not lightly suggest rehoming him.  I can imagine how heart-breaking
this must be; however, in his own way your cat has started to part from you.
This may not be irrevocable, and it would be great if you could turn things
around.  If, as a family and with both cats' cooperation, you can't change
this behaviour, then I really think rehoming is the kindest option.  Your
outdoor cat is now facing colder nights *and* fireworks - not a desirable
scenario.

I truly hope you can resolve this.  Please let us know how you get on.

Spider