We are thinking for about a month that she will stay there in home country and then come back after a month. Do you think if that works?
Only CBSA will determine whether it will be an issue. In general a month out of the country is not a lot after a long stay. A supervisa does not allow someone to permanently move to Canada. A one month visit appears that you are only visiting your home country. Given the fact that there was a significant overstay I would personally consider staying out of Canada longer but there is no way to know whether your mother will be denied entry, given a limited stay in Canada or have no issues.