25kph is simply too slow to be integrated into regular flowing traffic on an urban dual carriageway.
I cycle on urban roads at that sort of speed - and below - all the time (various bicycles, sometimes with a trailer, sometimes a recumbent trike). IME the multi-lane dual carriageways[1] are somewhat better, because the motorists have another lane to perform a proper overtake in. But as I said above, I'd try to avoid the Derby Ring Road.
[1] This sort of thing: https://goo.gl/maps/HNks6EaUzo72
I've noticed your judicious cropping of my post.
I seem to be making a habit of it.
Perhaps I shouldn't have economised on words and emphasised that my particular point about speed integration follows on from the previous sentence about wide vehicles. On most urban roads it is perfectly okay to ride a bike at lowish speed if your lane placement is appropriate.
I assume you don't have experience of wider cycles then?
What most people who do soon realise is that while the overall envelope isn't actually that much wider
[1] than that of a typical flat-barred bicyclist, drivers react quite differently, and give greater amounts of room when overtaking. Typically you get proper car-like overtakes, rather than attempts to squeeze past in the same lane.
(I suspect that much of this effect is down to being unusual and therefore subject to more careful observation, rather than the perceived difference in width. It's also why I generally feel safer in traffic on a recumbent bicycle than I do on a Brompton.)
I'm firmly of the view that the best way to further road safety for vulnerable users is not to unduly hamper other road users (check this link from another place).
I'm more pragmatic than that. Sometimes staying out of the way is the safest option, other times it isn't. I'd certainly say that *antagonising* other road users is to be avoided, except where necessary to ensure your safety (for example, I'll take primary rather than ride into a pothole or be squeezed at a pinch point), and I'm a big fan of letting the entitled arseholes get past you as soon as possible.
Besides everything else, I would be bricking myself if I found myself plonked onto a busy A38 in Brum (or Princess Road) on a trike or a mobility scooter. If you're not as chicken as me, then I can only wish you good luck.
From my own experience, riding a tricycle on the Bristol Road is pretty much the same as riding a bicycle with a trailer on the Bristol Road, which is pretty much the same as riding a bicycle without a trailer on the Bristol Road. I don't have a mobility scooter, but assuming it was reasonably engineered and I was confident with the controls, I wouldn't expect it to be much different.
[1] Although a multi-track cycle will sometimes need more room than a bike to keep the nearside wheel clear of gutter hazards.