Hi Mona, I agree with
@snganu. I have a similar case as yours. When I landed as PR nearly 6 years ago, I got my mom to Canada on Visitor visa. And then file for extension in 5th month. The extension is easy to file and can be done online. I always get extension for 1 year (thank god). Then send my mom back to India before extension expires for 3 to 6 weeks. And do the same thing again. She is with us for last 6 years like this and by god's grace, her PR is now in process in 2019. Going to US does not extend the stay, so your mom will have to return to India after every 1.5 years. All the best to you.