mduell

United.com is the wrong tool for you; it's not the worst airline website fare search I've used, but it's dismal compared to the independent tools. None of the tools will actually list all of the options, but two tools will get you what you want on a shiny 016 ticket: ITA Software's Matrix (matrix.itasoftware.com) and Hipmunk (hipmunk.com).

Start at itasoftware, multi-city search, and click "Advanced routing codes" so it gives you the extra box for options.
- For flight 1, the origin is "SFO", the routing code is "ua" (a single flight on United), and the destination is "IAH". Pick your date, choose preferred times to limit the departure to the time range you want.
- For flight 2, the origin is "IAH", the routing code is "ua :: / aircraft t:787", and the destination is "LHR". Pick your date.
- For flight 3, the origin is "LHR", the routing code is "o:ei" (a single flight operated by Aer Lingus - we do the o: operated by notation to allow codeshares), and the destination is "ORK". Pick your date (the next day, when you arrive in LHR).

Do the same to build up your return and hit search. When you get to the results, click on Individual flights or, my preference, Time bars. Pick your first flight at the time you want, pick the dreamliner flight for the second segment (and note it's arrival time, about noon typically), then pick the flight you want from LHR to ORK (looks like there's a 2p and a 6p). Pick your return segments to get to the final itinerary details page. ITA Software doesn't sell tickets, so we have to head over to the chipmunk now.

On hipmunk, you can use parts of the ITA route language (but not all of it), so we'll use the flight numbers you already found to constrain the search. In the from box enter "SFO :: UA1211 IAH UA4 LHR EI715" or whatever flights you found for your outbound, and in the to box enter "ORK :: whatever you found for the return". Pick your dates, search, pick your flights (they may throw in some weird options with like 26 hour layovers, just pick what you wanted), and then click on the "Book at United" button in the popup at the end. This drops you into the United.com booking process so you can purchase your ticket from United and get PQDs.

See this flyerguide page, this hackmytrip page, and this google faq for more details on the ITA advanced route language.

That said, you have some impossible requirements unless you take an overnight stay. The 787 IAH-LHR leaves around 9p, which means you need to be at IAH no later than 8p, which requires leaving SFO about 2p.