UPDATE
I ended up choosing to fly back from India via Abu Dhabi using Etihad Airlines. There were absolutely no issues. We were issued boarding passes for both legs of the journey (India to Abu Dhabi and Abu Dhabi to US)from India itself and the airline employee at India didn’t not ask me for any documents. I just handed over my Canadian passport and the US passports of my husband and baby and she gave me all the boarding passes (I guess she knew the preclearance in Abu Dhabi would stop anybody without proper travel documents from boarding so Etihad is fine). At Abu Dhabi I didn’t have to see the Check in staff as we had our boarding passes and so went straight to US Preclearance. That was easy too. the officer asked me if I had a green card as I only presented our passports first. I said yes and gave the expired GC and the original of the extension paper. He gave me back everything within a minute and we were off to board our flight back home. Only at the Gate while waiting I realized, I hadn’t shown him my marriage certificate (the GC and extension letter has married name and passport has maiden name). He didn’t ask, I don’t know why. Oh and though I had a very easy pass at the Preclearance, my husband who is a US born citizen was ‘randomly ‘ selected for extra security checks at the US Preclearance 😁. I thought that was funny!.
I wanted to post this update for anybody else traveling to India in my situation (expired GC+extension letter+ married name on GC & maiden name of passport). I would suggest to go through Abu Dhabi while flying back, if possible. Also regardless of which route you take, please carry with you all the documents (with copies) that the knowledgeable people in this thread suggested to me. I did.
Thank you to all the good folks who jumped in and promptly responded to my post with valuable suggestions. I was worried before I posted here, but you guys put me at ease with all the suggestions and I was able to travel with much confidence. Thank you all.