1999 £2 Coins Stamped Backwards?

What coin?

It's post mint damage - the middle has been pushed out and put back in again.
It is impossible for the mint to make this error - as the middles and rims are put together before they are stamped.

No, the two pieces are not stamped separately. The bimetallic blank is fed into the coin dies just like a regular blank is, and the entire coin is struck all at once.

The two pieces of metal, the core and the ring, are difficult to separate - but not impossible. Extreme changes in temperature can help, as the two metals will expand and contract at different rates.

Of course, if someone has a £2 coin that falls apart on them, they're going to want to try to put it back together, since nobody at the shops or the bank is going to accept it in pieces. And whoever put this one back together either wasn't paying attention to "which way around" it was, or someone was simply trying to be funny and deliberately put it in backwards.

Either way, it's a damaged coin, not a mint error of any kind. Sorry.