"Your Dad leaves Friday" was not accepted; I don't think the addition of "on" in English means any different.
Adding "on" converts this sentence from US English, which omits certain prepositions (a possible influence of German Americans on the language of the USA), to UK English, which doesn't.
Whilst I'm here: "leaves" is ambiguous in this sentence.
If the intended meaning is "begins his journey", it's safer to use the unambiguous "depart", because otherwise the subtext is:
"Your Dad leaves on Friday" to live with Gran and Granddad for a while. He needs some time by himself to think things over. – No, we're not getting divorced...
I think with "odjeżdża", which doesn't seem to be the best choice in my opinion, "departs" may indeed be the best answer. Changed now.
I believe omitting 'on' it makes it informal, but I guess it's okay here. Added.
We want to keep 'Present Tense in the future meaning' and the real Future Tense separately, because in Polish it really isn't that obvious when you look at the verb.