I want to add a 220 V outlet in my garage for a MIG welder. The problem is that I have only 1 space ( 1") left in my electrical panel. All 2 pole breakers that I have seen, with a single trip, take up 2 full spots on the electrical panel. I really dont want to start moving things around in the panel if I dont have to. My question is: Could I use a 20 A tandem breaker that takes only one spot in the panel, and run the 2 hots to it? Furthermore; is there a way I can make this tandem breaker single trip for safety and correctness? Can I buy or make a "tab" if you will, to make this tandem breaker trip together should a problem arise? I thank you in advance for your help. I currently have Cutler Hammer type BR breakers in the panel if that helps.

No. The tandem breaker uses only 1 phase of the panel... you will have 120 to neutral from each one, but since they are on the same hot leg of the panel, you would have nothing between them. You may be able to get another tandem breaker and free up another space for a true dbl. pole breaker.

Yes but I don't think I was clear