In that case, yes you should just get your wife do all the translations/notarizations for you, and make sure she has all the docs and send them all at once to you. Don't need to extend your stay, its a waste of money. You don't need to be in VN for her to translate/notarize. You will get the medical document from IOM on the same day she goes in for the medical (the medical only takes like 1.5 hours, you will get the document right after she's done). Don't lose it, it's your only copy. According to CIC, the criminal checks have to be done at the Provincial Justice Department where their permanent residence is, I would guess that means where she is currently living. For me it took 4 weeks to get it, but I think it was because they dont work on Tet holiday, and we applied for it before Tet. I'm not sure how long it will take for your wife, depending on where her permanent residence is.
Your dad is wrong, you the sponsor, do not need a medical exam. You only needed it when you were trying to apply for a marriage certificate to marry your wife in Vietnam.
I think with only 3-4 days left, you dont really have time to gather the documents yourself, she will have to mail them to you. Make sure she pays for the fastest shipping possible, because you don't want your documents to be in limbo during transit. One thing I highly recommend you do now that you're in Vietnam, is ask her parents, siblings, friends (not all of them), to write you letters of support in vietnamese, then get your wife to translate and notarize them. They are good in strengthening your wife's PR application.