Chances of success with the visitor's visa are low as well unless she can prove significant ties to her country that will make the visa officer believe she will return to Pakistan after her visit is over. If you intention is to get her here and keep her here until the sponsorship is finished, chances of your success are very slim.
You can't lie to immigration. She has to identify all of her family members so the visa office will know she has a daughter in Canada even if the letter of invitation comes from someone else. She will also be asked questions during the interview for the visa and if she lies, that's misrepresentation on her part which will automatically prohibit her from entering Canada for 2 years. You don't want that on her file if you are applying to sponsor her.
You can't lie to immigration. She has to identify all of her family members so the visa office will know she has a daughter in Canada even if the letter of invitation comes from someone else. She will also be asked questions during the interview for the visa and if she lies, that's misrepresentation on her part which will automatically prohibit her from entering Canada for 2 years. You don't want that on her file if you are applying to sponsor her.