There you go, one ticket is the way to do this (so many people buy two tickets then have quite a faff as a result) . It is interesting to note that WS does not have a baggage interline agreement with LA but LA has one with WS. WS has a tiny interline list. You'd think these would be reciprocal arrangements. Thus it is theoretically possible on the way there WS can't or won't and on the way back LA can and will. How odd. I think WS will check the bags through. And that's because....

WS has a couple of LATAM codeshares LA5180 and LA5178 that are the same actual flights as WS1698 and WS1696. Did your travel agent issue it all as LATAM? 045 is a LATAM ticket code (WS would be 838). Either way it's clear that if WS operates a LATAM codeshare from YVR they will work with the bags as if it were a LATAM flight. I think you have a LATAM ticket with the WS codeshare on the way to LAX and then LATAM onwards.

The reservation (locator) codes are airline specific so you can for example view your flight or change seats, etc. LA would want their code to let you do that. And WS theirs.