いちいち腹のたつことを、わざわざ言いにこないでよ
Don't come specially to say things which make me angry (my translation attempt)
I'm confused by 腹がたつ. It's my understanding that it means 'to get/become angry' rather than 'to make angry'. How can I understand what's going on here?
More generally, how do I say things like 'That person makes me angry' or 'Eating cake makes me happy. I include both examples because I suspect that people making you feel things is different from things making you feel things.
My gut feeling is that the cause of your confusion is the true transitivity of the idiomatic expression 「[腹]{はら}が[立]{た}つ」. You already seem to know it is intransitive in Japanese, but you rightly translated it as if it were transitive -- "things which make me angry".
Of course, you could have translated 「腹の立つこと」 as "things that I get angry over" or the like and the original transitivity would have been retained. In translation, however, whatever sounds better in the target language is the better translation.
You have achieved a good translation at the cost of a Japanese intransitive verb getting unduly treated like a bloody stupid transitive one. That kind of thing, however, happens all the time when translating between two unrelated languages.
At least, the above is what the average Japanese-speaker with a weird French username thinks is happening here.
"More generally, how do I say things like 'That person makes me angry' or 'Eating cake makes me happy. I include both examples because I suspect that people making you feel things is different from things making you feel things."
This is highly related to what I have ranted about above.
In natural settings, Japanese-speakers would not say the directly translated versions of "That person makes me angry." or "Eating cake makes me happy.", period.
The direct translations I am referring to would be:
「あの[人]{ひと}は[私]{わたし}を[怒]{おこ}らせる。」 and
「ケーキを[食]{た}べることは私を[幸]{しあわ}せにする。」, respectively.
Again, we would practically never say either of those in a natural setting. You would undoubtedly sound like a robot if you used those sentences in real life with a native speaker.
We do not use causative verb forms to express those feelings in Japanese. We would instead use sentences such as:
「（私は）あの人に[怒]{おこ}っている。」
「（私は）あの人に腹が立っている。」
「ケーキを[食]{た}べていると[幸]{しあわ}せな[気分]{きぶん}になれる。」
「ケーキを食べている[時]{とき}が[一番]{いちばん}幸せです。」