She can leave the 2nd child with you, not alone? She would however have to stay for 2 years straight before she can sponsor you and the child and that is only if she is allowed in in the first place without getting reported.
If this is not an option for you, you have the same opportunity to apply for PR again as everybody else. The immigration classes or rules may have changed since you applied the first time. You will have to check the CIC website and find out if you qualify for anything, see http://www.cic.gc.ca/english/immigrate/apply.asp
Before you apply for a new PR, you must first officially renounce or lose the PR you currently have. You can take care of this by applying for travel documents, see http://www.cic.gc.ca/english/information/applications/travel.asp You should write on your application that you are not actually requesting a travel document as you know that you do not meet the requirements and that you wish to renounce your PR so you can apply again.