Welcome to flyertalk brtennis.

You put yourself in an interesting situation.

Your 2nd paragraph is where the gap in understanding lies. When you book via the UA website, you are subject to UA rules, and using UA MP miles. UA basically pays no mind to one trying to use another airline's miles. US basically pays no mind to tickets that didn't originate with them. That US flight on UA ticket stock is by definition a code-share.

The story may change and become negotiable when you get to the airport and show your US miles for the US metal (i.e. aircraft) flight. I don't have experieince with this personally.

In your 3rd paragraph, the point that the agent didn't make clear to you is, even if you had a US-purchased ticket, the class of fare determines how far ahead of your flight you can confirm an upgrade with miles. In general, the more expensive the coach ticket, the more likely you can upgrade ahead of time.

In hindsight, if you could have purchased the US portion on the US website (one-way), and the UA portion on the UA website, that would have given you the best flexibility.

Good luck. I would personally spend the miles on an international ticket, as that extracts a proper value for them. You can educate yourself here for tips on that.