I have tried to ignore their attempts, knowing their intentions, but it seems to the others that I am establishing a double standard. I am really at a loss. I have talked to the pair about their behaviour and referred the issue to their personal tutors but the problem persists.
The really hard thing is to remember they are just children. Clearly, you have reacted in a way that appeals to them - and they now want to get this reaction again at any price. Losing your rag, as I suspect you have done, is the start of a slippery slope but not a slope you can't get back up.
In the end, if you are fair, set out clearly the sanctions for bad behaviour and point out that they ultimately have the choice to either follow the classroom rules or face sanctions. Then you may win back some ground. You will need wider support, though, because the ultimate sanction may be exclusion.
There is no reason for it to go that far though. Importantly, do not demonise these children. If you have sanctioned them for one incident do not allow it to taint the way you continue to teach them. If a child thinks you do not like them then you can't possibly hope to win their trust and, without that, teaching is a dead end. Separating personal feelings from teaching is the hardest thing of all!