Yeah you should tell them, because they will know either way.
The 20 days won't matter, its ok as long as you file the extension before her status expires, in the mean time she will have implied status.
However, in terms of parents they likely won't accept an HC application due to a person being a widow. To get an HC application approved is very tough, you must show very exceptional reasons, you must also show you have established strong ties in Canada, since your mother has only been here since June, it'd be very tough to do.
I don't mean to be rude, I'm sorry, I just wanted you to have all the proper information.
I would read this first
http://www.cic.gc.ca/english/information/applications/guides/5291E2.aspPlease also read this for useful tips and suggestions.
http://www.visaplace.com/canada-immigration/humanitaran-compassionate-applications.php