OK, pater - I know you're honestly wanting to do the right thing, but you've gotten caught up (like alot of people) in language on the CIC website that (whether it's intentional on their part of not) is misleading you about how this process works and about what the right thing to do actually is.
First of all, what ariell has said about inland v outland is correct.
Every foreign national has the
right to have their application processed at the visa office that represents their country of birth - regardless of where they may be living or visiting (including Canada) during processing. CIC cannot force someone, just because they're in Canada, to file an inland application because that application does two things: it requires you (as the sponsor) to forfeit your right to appeal a refusal, and it forces the applicant to remain in Canada throughout the duration of processing because it requires that the applicant be residing in Canada with their spouse/sponsor in order to be approved.
In addition, the inland process will NOT rectify your wife's overstay! In fact, your wife's overstay actually complicates an inland application - it means that it cannot and will not be processed at the Case Processing Centre in Vegreville within normal processing timelines (which would result in her receiving first stage approval - and new temporary status - within 6-7 months). Instead, your ap would be transferred to your local CIC office for processing BEFORE first stage approval, and would become subject to the local office's timelines. Some local offices are backlogged in excess of two years! That means that not only would you have "tipped them off" to your wife's overstay by filing an inland application, but they would then, basically, hold her PR hostage over it, and leave you guys sitting with 1) her still not having legal temporary status (which means she could be deported), and 2) no options for rectifying that by leaving Canada because, if she left, she'd likely be unable to return and then she wouldn't be able to meet the inland requirement for residing in Canada in order to be approved. This is what you'd be facing if you filed inland. And, as you see, filing inland is also a bad idea in your case because she's already intending to leave Canada to be with her mother. If she can't get back into Canada, your inland ap (and the fees, and the medicals and everything else) is gone! There is no guarantee that she will be allowed to re-enter Canada - in fact, if she is
non-visa-exempt it's likely she will
not be able to get another visitor visa to come back to Canada . . . simply because she is married to you. It seems really screwy, I know, but being married to a Canadian means that she will be absolutely unable to convince them that she honestly intends to visit Canada temporarily, and that means they will be unable to issue her "temporary" status. If she's visa exempt, that situation changes - but you'd need to accompany her on her re-entry.
So - your best option for a successful and expedient application is an outland ap. You need to understand two things: first of all, the processing officer at the overseas visa office is not concerned with whether or not your wife has overstayed in Canada . . . even if she wasn't going home to visit her sick mother. In addition, once she DOES leave Canada, she is immediately in compliance again . . . the overstay is erased. So you don't have to make explanation for that - it's over the minute she leaves Canadian soil. Right now Immigration Canada is completely unaware of her overstay - it does not need to be disclosed, and won't be disclosed unless you make the mistake of filing an inland application! Secondly, you don't have to wait until she leaves Canada to file the outland ap. There is absolutely NO requirement that an applicant has to be physically outside of Canada to file an outland application. The sooner you get that application in process, the sooner she's back with you as a landed immigrant. (If you let us know where she's from we can tell you which visa office will process her ap and what their processing timeline is.)
Obviously there's a lot to consider here - so please write again with any more questions. You're also welcome to email me, if you like. Just don't back yourselves into a corner here thinking that you're required to file inland if she wants to be in Canada - and secondly, assuming that her re-entry to Canada is a given because of her marriage to you.