Don't be afraid of using a little heat, it'll do the job.
A tire store will have a tool like this one that will remove damaged lug nuts or locking lug nuts.
Snap on This one of the most affordable and useful tools in my shop. I use one at work and at home. It is easier than using the acetylene torch at work and usually puts out enough heat for light duty jobs like lug nuts. Real handy for lighting fireworks and bottle rockets too.
Good luck, between hammering on a old socket on it and some heat it should come off with a breaker bar. Have never owned a dremmel tool, too light duty for me.
