It does not matter who mined the 12 blocks. If you want to double spend a coin in 12 blocks before (say current block height is 10012, and you want to double spend a coin at 10001), you have to reverse back 12 blocks and begin mining a new block (10001). In the same time, other miners are mining 10013. Your hash rate needs to be faster than all other miners so you can catch up with the main chain before next difficulty adjustment. Don't expect you will finish all blocks 10001 - 10013 before other miners find their block 10013. You have to catch up with them slowly, maybe at block 10033 or even 10133. Before that, all the blocks you mined are treated as orphan blocks.

If you are still mining the shorter chain after next difficulty adjustment, you will never catch up because the other miners mining speed will be doubled due to difficulty decrease.

Moreover, it is very easy for the public to find you are trying to do this malicious thing.
1) The confirmation time of following blocks are doubled, because your hash rate has left to mine a 10001.
2) You've mined many orphaned blocks in a row (10001, 10002, ...) until your chain catches up with the main chain and replace it.
3) All the clients will suffer from a deep reorganization after your chain finally catches up and replace the old block chain.

In short, even if you have 51% hash rate, you will not double spend some coins 12 or even 6 blocks away. Otherwise, it takes a lot of time for you to catch up with the main chain, and people will notice this very easily.