First, let's see what the difference is between your first two sentences:
Deseo que estés aquí = I want you to be here.
Yo desearía que estuvieras aquí = I wish you were here.
The first sentence comes across as quite assertive. The second acknowledges that it's impossible for you to be here (for example, maybe you're out of town). But note that although this is technically correct, a more natural way of expressing this would be
Yo quisiera que estuvieras aquí.
which means the same thing but is more comfortable to pronounce.
Now for your questions. "Desearía" sounds weird, and "quisiera" is a special case, so let me explain it with a different verb, pedir:
(a) Te pido que hables con mi hermano mañana.
(b) Te pediría que hablaras con mi hermano mañana.
(a) is more direct, (b) is more gentle. It's just a difference of tone.
Now, how can the tenses be safely combined in one sentence? There are two patterns to choose from:
{present} ... {present subjunctive} e.g. Pido que hables.
{conditional} ... {past subjunctive} e.g. Pediría que hablaras.
If you want to have a slightly similar construction in English, as motivation for the combination conditional ... past subjunctive, you could think (very loosely) of this:
I would have liked you to have spoken.
Of course it's not the same but it could possibly help you build some intuitive feel for the pattern.