Is it possible to target the compilation to another family of microcontroller rather than AVR?
Did anybody have a clue what do I have to change in Arduino IDE in order to generate code to a 68HC08 ?
Well actually it not the IDE that would require the most changes, but rather the whole tool chain included in the arduino IDE distribution, which are not even developed by the arduino team. So you would need a 6HC08 compatible C/C++ compilier, linker, and libraries as those are AVR processor specific. Also a new uploading program would have to be found or created as AVRDUDE is AVR processor specific.
In the bigger world of microcontroller in general the arduino IDE is not consider all that powerful and useful an IDE compared to other open source and commercial offering, some of which might already support the 6HC08.
What your asking for would take a very large effort with little advantage over other solutions I bet.
I suspect your best path is to seek out a microprocessor forum that deals with the 6HC08 processors and find out what they use in the way of an IDE and other needed tools.