Given that EI business class allows FL access at ORD, I'd be shocked if AA didn't let you buy FL day passes with a departure on EI, especially in your situation where some members of your party have access and some don't.

Yes the rules technically say you must be on a oneworld flight, but the EI access is a niche case, we've seen plenty of instances where what AA publishes doesn't match up 100% with reality.

I would give it a shot if you really want access. You would for sure have to buy 2 passes at $150 each for you and your wife, YMMV on whether they'd also let in your 2 kids, probably given they're both under 2 but that would ultimately depend on the agent.