"I am coming with you to the Rhine."
Translation:Ich komme mit dir zum Rhein.
In fact, this thread from a while ago is super useful... https://forum.duolingo.com/comment/22892271/What-s-the-difference-between-zu-and-nach
"zu" is a preposition that signals the beginning of what is referred to as an "adverbial phrase". The noun object that comes after "zu" is not an object of any verb; it's an object of "zu" itself, and is thus indirect. Google "adverbial phrase" if you'd like a lesson on the structure in English. It applies similarly to German, you just have to remember which prepositions start one.
I - me -- ich - dir/dich
you - you -- du - dir/dich
he - him -- er - ihm/ihn
she - her -- sie - ihr/sie
it - it -- es -- ihm/es
we - us -- wir - uns
you - you -- ihr - euch
they - them -- sie - ihnen/sie
you - you -- Sie - Ihnen/Sie
It's not the fault of German that English puts so many different meanings in the word "you" and does not differentiate between subject and object case, as it does for most of the other pronouns.
The separable verb "mitkommen" exists indeed, but it cannnot have an object or the like. So "Ich komme mit" means something like "I come along". When all the others go to the Rhine, you can say "Ich komme zum Rhein mit", when you want to participate.
But here you don't use "mitkommen", but simply "kommen", and the "mit" is a preposition that belongs to "dir". "mit dir" = "with you". And, like in English, prepositions directly precede the word they refer to. So you can't separate "mit" and "dir".
When you type "I am coming with you to the Rhine" into Google translate, it gives you, "Ich komme mit dir an den Rhein". Duolingo marks this as wrong. Little frustrating. I guess because they haven't taught me "an" yet and it's a dative preposition lesson. But, it shouldn't say it's wrong if it's a valid translation. It should say - another option is....