Coco.
Make no mistake, you can be replaced. This is not a put-down, I'm sure you're excellent at your job.
From a managerial perspective, the question is: Can this position be filled for the wage? The answer is always YES.
They may (probably will) have difficulty for a period of time gaining an equilibrium that you provided if they replace you with a new guy. But that new guy will have some experience handling and running machines. The supervisor chick will have to get more involved to pick up the slack. But the show will go on, and in six months, it'll probably be basically the same (again, from a managerial perspective, quotas and etc.)
There is a certain amount of flexibility you can extract from management. As mentioned, if you show them you've been offered a reasonable raise for employment elsewhere, they may match it if it is not outrageously higher. I would peg that number at around ten percent. So in a serious bargain, you could possibly get a $1.05 raise. Over the six months that they would be inconvenienced, this would add up to 1,040 hours at the increased wage, and on into perpetuity.
Your raise would cost them about $2,000 per year. Future raises are calculated from that higher wage. Next year, you get another 3%, it would be based on the 11.50, and so on, and so forth. That compounds to around $9,000 increase spread across three years. (you'd go up about $1000 per year anyway, plus the 2000x3 = 9000) - this is why bosses want to kill your face when you want a raise.
Other workers hear this, they want a bump too. Labor is already calculated as a rising cost.
Knowing all this, I would tell them I want the Lead Supervisor job, if you're sure you can do it, and you would personally train the replacement for the position you are vacating, who would assume your role at the wage you are currently earning - thus, the transition would cost them nothing they aren't already expecting.