XPS 9550 Battery Problems

I have an XPS 9550. Over the past few months, my computer has been randomly overheating when turned off. There was a distinct burning smell and I was burnt touching the metal case. I contacted Dell support multiple times. They insisted it was a software issue. During this same time, my trackpad was slowly losing click functionality. 

Today my computer overheated AGAIN and my trackpad lost all clicking functionality. It also started popping out of the computer. Looking this up online, it seems that this is all related to a known safety and functionality issue with the battery for XPS 15 9550s. 

Calling support tonight they immediately agreed to fix the battery free of charge but insisted I give up my computer for 2 weeks. There is a known safety issue and I was not informed as a consumer... yet I still have to go without a computer for 2 weeks? Has anyone figured out a way to get it repaired without going without a laptop for 2 weeks?