Hi Spirantho and J-Golden 
Firstly, thank you for your thoughts, and please accept my apologies for not replying immediately. With two kids and all and work... yadda yadda... :juggler:
J-Golden, thanks for the good suggestion of setting the bios. I hadn't thought of that, and it was set incorrectly. I've fixed that now - that info alone should get me one step closer to success with this. 
'fraid the BIOS setting is just for the on-board - won't affect the Catweasel at all. You should have the BIOS set to just what is on the motherboard connector - probably 3.5" drive A and nothing else, maybe not even that.
Spirantho, thanks for the assurance about not having to mod anything. That's good news. It's good to have you there - you must be the most qualified person on the planet to help me through this. :laugh1:
I think Jens is more qualified than I.

He made the hardware!
I haven't managed to get this working as yet, however I have purchased a new, longer floppy cable this afternoon which supports 5 1/4" and 3 1/2" floppy drives and is 0.81m long allowing me to get both drives connected at the same time to the Catweasel card. I suspect the floppy cable I am currently using is faulty. The new cable will arrive in a week so I'll come back to this good forum and report back my findings.
One more potential problem to discount; that's good.

Just out of curiousity, are there any 5 1/4" floppy drives on the web for sale which are specifically compatible with amiga formatted 5 1/4" floppy discs?
The whole point of the Catweasel is that you can read anything using standard drives, so don't worry, you don't need anything special unless you're running directly on an Amiga.
I am pretty sure the OS I was using on my old Amiga 2500 was OS3. It had a built in SCSI drive and I was using an external 5 1/4" drive to backup my song data. It's the same drive pictured in the photo here:
http://mc9.co.uk/amiga/drives.html
And is it at all possible to transfer data using Amiga Explorer / Serial Cable between an A500 (with an attached 5 1/4" drive) and a PC if the data on those 5 1/4" floppy discs came from an A2500 running (i'm guessing) OS 3?
As long as the A500 is also running OS3, or the disk was formatted with OFS (not FastFileSystem) you should be able to read it yes. I have no experiene with AF, but TwinExpress would do just fine, you could probably even use SerNet and access the floppy as a shared drive directly within AF!
Simplest way would just be to use an Amiga to copy to PC-formatted disks, though!