The only thing with getting a new key fob is that they will send you new cards as part of the package, so you have to swap everything over.
Plain wrong.
If you ring them, they'll happily send out additional cards or keyfobs.
Any new cards they send out will be linked to your old one, and it's perfectly fine to use either one, as all the points should go into the same 'pot'.
If they're not, it's usually because the operator has managed to create an additional separate clubcard account (These also sometimes get created by credit cards/ savings accounts). In this case, you need to ring them with your name and details, and ask them to do a search for disassociated Clubcard accounts in your name, which again they'll then be able to link into one 'pot'.
Final note, treat any quoted timescale with a large pinch of salt. Normal times are about 4-6 weeks to sort out any new/ replacement cards, despite the 2-3 weeks quoted.
(I work for Tescos, although instore)
-Leezer-