How do we know that we have to use "dafür" in this sentence? Why "dafür" and not some other "da-word"?
Ich will auch, dass du glücklich bist, aber nicht genug, um etwas dafür zu tun.
How do we know that we have to use "dafür" in this sentence? Why "dafür" and not some other "da-word"?
Ich will auch, dass du glücklich bist, aber nicht genug, um etwas dafür zu tun.
You're confusing verb constructions with the same verb here.
It's true that there is
mit jemandem/etwas zu tun haben (to deal with someone/something)
In your above sentence, there is no haben though, which is crucial in this construction. Thus we can rule this out.
Another construction with tun is
etwas für jemanden/etwas tun (to do something for someone/something)
So a way to identify the correct da-word would be to start backwards. What do you want to say in English, find out what the appropriate (infinitive) form in German is and then find the corresponding da-word.
Addendum:
There is also
etwas gegen jemanden/etwas tun (to do something against someone/something)
which would then require dagegen.