Hey Samaran04, AFAK, a job offer is not necessary to get the PGWP based TRV. You just need to prove that you have enough funds to support yourself in Canada.
I read your message in my inbox and yes, you should use your mother's bank account information to prove that you have enough funds (because you do not have a current valid job offer). In addition to that, You could also, print your Canadian bank account statement and attach that as a supporting document but you wouldn't have any means to get it verified (like getting it stamped by the bank -teller) but I was in the similar situation and I attached them anyway and gave an explanation in the appendix. It's not required but you can attach it, it's up to your judgment.
About the part-time job that you held before coming to Canada - Since you are no longer employed there, that can't be considered as a source of income.
I submitted my application at VFS Delhi office, they just gave my documents a cursory look, it wasn't very helpful.
I wouldn't rely on VFS guys to review my documents. It's a rather straightforward application so don't worry about it too much just get your documents in order, according to the checklist. feel free to post your questions here, I will try to answer them the best I can.