Assume you are aware that focus is critical.
I suspect much of your issue, is it’s only a 2W IR source… Switching from a chromed tool to a mug might mean you have to really slow it down for removal of a mugs coating. There is a difference in marking something, compared to removing a coating.
Take the speeds you’re using and compare them to you 10 or 20W visible laser. Both should have similar absorption rates. If your 20W machine worked on mugs, I’d slow it down 10 times.
A 2W is only 1/10th of a 20W module… just because it will absorb IR, doesn’t mean you can run fast.
Might want to read this post on mugs with a normal laser, you will have to run slower… and might need to use a smaller interval. He mentions having to slow down to the 50 - 100mm/m speeds with a 10W machine. That’s only 5 times more powerful.
If you cut the interval in half, the job will require twice as long to complete.
Good luck