Correct on both counts
avionic-type.
The VC10 was modified to test the RB211 but with an engine mount that mimicked the Tristar installation. This was visible as the pylon-like bit above the engine. This installation was quite heavy and wouldn't have made the VC10 any more economic than it already was. As you mention, the fuselage turned out to be distorted at the end of the trials so G-AXLR/XR809 never flew again. More info and photos here:
Histories - XR809
SSD: As I said before re-engining just isn't profitable for a small set of airframes. Also in those days ETOPS was something very new, a twin engined-VC10 would for a lot of operators have been a very unattractive proposition as it limited its routings. And getting such an airframe into ETOPS regulations then would have meant far more modifications!
As for the Trident, it was originally going to be a larger airframe with RR Medway engines. BEA wanted it scaled down and so they did. In the meantime Boeing had a look at the original specs, built the 727 to match them (approximately, the story is a bit longer of course) and the rest is history.