For me, both next sentences are correct :
- I don't want you to go to Ireland.
- I don't want that you go to Ireland.
How do I know whether or not I should use "that" in a sentences like these?
Some verbs, can be followed by that clauses, some cannot.
There's no easy way to decide if a verb is followed by a that clause or not. Mostly, you'll have to learn them as part of a phrase.