Ok, got it now! My motors are pulling about an amp on a 5V supply so a PP3 with its 9V 500mAh capacity would soon fail! Thanks for the explanation. I'll bin the PP3 battery connection that came with the Arduino pack and stick with plug in PSUs.
The second motor still doesn't work though! And we're about out of suggestions here so I'm wondering if it's a wiring problem on my breadboard. I was toying with the idea of making up a soldered stripboard version to try. But I think I'll abandon the bait boat project. You can get one on Ali Express for £60!
But it's not been a waste, I've learnt a lot. Thanks.
I have tried swapping the motors, they both work ok on the left side. I've tried rotating the IC 180°, (both voltage pins at 5V) and trying another IC, the problem is always on the right side. I've tried swapping the three data connections for each motor. All to no avail! I think it's a connection problem on the breadboard. But when Ali Express put an advert on my screen for a bait boat for £60 after a YouTube search for bait boats, I abandoned the project.
I might come back to it just to get it to work but I won't be building a bait boat. I've moved on to a relay control project now so that I can switch the power in my observatory remotely, from indoors, through TeamViewer.