United upgrade pecking order is complicated.
to determine upgrade eligibility for the international segment using miles upgrade, are we going to be given priority per the booked class for that segment (Y, which is higher) or V (which is substantially lower down).
It's Y since that's the fare class of that segment.
However since "Y" is an economy fare, any upgrades from Premium Plus (O, A & R fares) are upgraded first.
My wife and I both have MileagePlus Premier Silver status.
Unfortunately, that's a problem. Status trumps fare class, so any Global Services, 1k, Platinum & Gold members will be upgraded before you. You will be (by far) the leading candidate for Premier Silver passengers but that only will help if the upgrades work their way all the way down through Premier Plus and status.
I may be wrong here: A "Y" ticket is somewhat unusual. They are rarely purchased directly since they are typically way more expensive than normal business class tickets (P, Z and sometimes even D). So it depends a bit on how you actually ended up with "Y" ticket.