can you request an itinerary or ask them a way you can obtain it? I assume you have your booking code or similar reference number?
It is weird they never emailed you the itinerary with flight times and such. It's not uncommon to need that info, my dad has to show when he was out of country and how long and purpose as he's on indefinite leave to remain (like a greencard) and he travels a lot for business. The record of you booking in more detail exists somewhere, I'm sure it can be provided or found online. I just included my itineraries instead of boarding passes as I only use digital.
Honestly, I think your partners boarding passes + proof of your presence in mexico (your card + photos + airbnb and whatever else) should suffice. Like theoretically not all LDRs fly to meet up so not everyone has boarding passes to prove they were together, they are prob the most straight forward evidence though.