Peels can be done at home and provide great results, but you really need to be careful and know what you're doing. If you go too strong too quick, you can really burn your skin and cause permanent damage.
The high price of the peels isn't just for the product, or even the location of the spa or whatever you are going to; you're also paying for their expertise. Unfortunately it isn't as simple as buying the same product as those used by the place that you use to go to and getting the same results.
I would never use professional strenght peel products on my face without the proper education. Use caution and common sense though and I'm sure you'll be ok.