Upvote:1
1) Your green card application: I had asked this to my lawyer and she answered the following: if you haven't applied for I-485 (change of status) yet, then technically you haven't shown immigrant intent. However, if the CBP officer can see that you have a pending/approved I-140 (immigrant petition), he/she can make a judgement call, and then it all comes down to his/her leniency. There are other factors that can affect this decision as stated below.
EDIT: I'm not 100% sure if they can see your current applications to USCIS (see link below). But I've heard from everyone that they do.
2) Your earlier entry denial: Why were you denied entry? Is that because the officer thought you did not plan to go back or your papers were incorrect? If you have traveled after that denial to US, and you haven't been banned from entering the US for 5 year or anything, then it likely won't affect your next entry. However the officer can see your earlier entries and denials so you may be taken to secondary questioning and/or denied entry. Again it comes down to the leniency of the officer(s) who question you.
3) Canadian PR: You have a Canadian PR, but you also have applied for US GC. The US CBP officers are usually not interested in your Canadian PR. Maybe it might prove you have ties to Canada so you can make your case to return, but then you also have applied for GC. The CBP officers might weight these two facts against each other.
4) Your job/lease/return ticket: If you had a ongoing job or a lease in Canada, or return ticket, that will certainly work in your favor if they take you to secondary.
5) Traveling with your mom: If you do get questioned, it might work in your favor if you describe the whole surgery situation to the officer. Your mom shouldn't have a problem since she has a GC. But you should carry all papers for the surgery so you can prove your are telling the truth, if secondary questioning if required. It again comes down to how understanding the officer is.
6) Traveling from India to US: In the end it's your decision, but if I were in your position, I'd spend some extra money and first fly to Canada, and then take a connection to US. Your mom is a US Citizen and you have a Canadian PR, so going to Canada should be a piece of cake and Canadian CBSA is a lot more lenient. Once you are in Canada, you can try to clear the CBP pre-clearance, eg. at Toronto Pearson. That way if you do get denied, atleast you're not sent back to India from US. In my experience US preclearance in Toronto have been much more quicker and friendlier than US CBP at PoE, say NYC. Also I haven't heard horror stories about Canada Preclearance, as I have about, say, JFK PoE.
EDIT: I had earlier assumed she is a US citizen but she has a GC. But that shouldn't be a problem as she doesn't need visa for Canada (http://www.cic.gc.ca/english/helpcentre/answer.asp?qnum=593&top=16)
Your situation is too complicated and there's a small chance that the officer will look at all your history and may cause problems. You've to weigh all these things and take a calculated risk.
Some additional info: https://www.quora.com/What-kinds-of-information-is-on-a-CBP-officers-computer-at-a-port-of-entry