If you're unsure about «īs», here it’s the second person present tense of «eo», to go. An educated Latin speaker may have possibly pronounced this vowel long to distinguish it from the demonstrative pronoun «is». In any case, «īs» from «eo» is marked as a long vowel (ī) in most grammar books.
That’s an interesting point. If you type «isne» in to the The Latin search engine http://www.mlat.uzh.ch/MLS/, you’ll find that most of the results seem to refer to «is» as in the pronoun rather than the verbal form.
In daily or colloquial speech they seemed to use the phrase «quo vadis?» a lot more, or at least we have some examples of the phrase in Latin literature.
The «is» was replaced by «vadis» from the verb «vādō»: this is still the case for many modern Romance languages: The Spanish verb «ir» uses voy, vas,va,van, etc. from «vado» but fui, fue, fueron, etc. from «eo».
Ambrose wrote it in his Commentarius in Cantica canticorum: «Denique Petro dicenti: Quo vadis?». Alcuin of York (8th century), in his De orthographia, says this: «Quo vadis, ad quem locum significat. Qua vadis, qua via dicitur», suggesting «ad quem locum [vadis]» was another way of saying it. [Where are you going? means to which place are you going to?. How are you going, you say by what way].
After all this rambling, I think «vadisne domum?» is a good option when asking a question, even if we’re taking about Classical Latin, for we at least are sure «vadis» was used, although using «īs» is still grammatically fine. I haven’t found an example of «vadisne» in Latin literature, save for a 16th century translation Xenophon’s Cyropaedia which has «vadisne igitur»: I also found this Latin syntax page which uses it: https://scholarisopus.wordpress.com/2009/12/31/syntaxis-capitulorum-xli-xliv/