Yes, UA will always show the lowest fare, given the restrictions of your itinerary (r/t vs. ow, min/max stay, date restrictions, etc.).Fare class availability is the other key, as mentioned. While you point to 'UA Express' as the issue, the bigger issue with UAX is not that they 'price higher' per se, but there are less seats. All else being equal, a mainline vs. UAX flight with similar demand will typically price higher on UAX, not because of 'UAX', but because the lower buckets are likely to sell out faster on, say, a 76 seat plane than a 160 seat one. Also, I've seen some routes where UA is operating UAX equipment where they probably should or could be using mainline, for example, SFO-PHX morning flight. That will fill more quickly, again, causing higher prices earlier on.

Same with peak dates. It's not that fares on thanksgiving are necessarily higher than other days (although peak day surcharges are certainly a factor), but people tend to book far out, so lower buckets disappear more quickly and are also probably more restricted, making it look more expensive if you didn't snag one as soon as those are available. I'm seeing super-high fares now for Memorial Day weekend, but my guess is a Fri-Mon itinerary this coming weekend, booked 4-6 weeks ago, would not have been nearly that high.