The correct expression is jusqu’au. I can’t think of many cases with two contractions: qu’au(x), more generally; also d’aujourd’hui. There’s no special rule about them. If there are two places to contract, and they happen to involve the same word, so be it.

Note that apart from au and du, it’s the end of a word that gets elided because of a following vowel; that doesn’t affect the beginning of the word. In the case of au and du, the contraction doesn’t affect what could happen to the preceding word, and no contraction is possible with the following word; however, au and du are not used when the next word begins with a vowel sound, so you could say that in that case, the contraction {l’ + vowel sound} takes precedence over the contraction {à/de + le}.

Most contractions are just simple elisions in French (one or two final letters are replaced by an apostrophe). Only four are non-trivial, each of them involve one preposition and one article (they don’t apply when le or les are pronouns):

• au = “à le”
• aux = “à les”
• du = “de le”
• des = “de les”

Those contractions are always performed, except when the article le, which is part of these compounds, can be elided first (example: de l’abandon, à l’abandon). This is actually the only point you should be careful about.

Now, because au, à or aux begin with a vowel, the word that precedes might also require an elision (but this was expected):

Jusqu’au matin.
Jusqu’à l’aurore.
Jusqu’aux premières lueurs du soleil.

In very rare situations, several elisions could be chained.