I found a bag of peat/sphagnum moss in my mom's magical cabinet. Then I sat outside waiting for the mail truck to come. An hour later, it came and I went out to get my lovely new cultivars, but to my dismay, they were not there. I'm having a ton of trouble making drainage holes in the plastic pots I bought yesterday too. I've tried a drill, but the plastic is too hard and the one hole I made cracked the whole bottom of the pot and sent the pot flying into the wall!
I WANT MY PLANTS!
Make sure that it's not the Miracle-Gro brand of sphagnum.
I got to replant a couple plants a month or so ago when I realized that I had made that mistake. The fertilizer in the sphagnum will kill them. If it is that, go with the regular sphagnum you have. Assuming it is actual sphagnum moss, that and perlite will work fine. But if the peat moss you have isn't tainted, that'll work great.
And actually, as someone pointed out, learning how to drill plastic is a bit of a trick. It's all about the pressure. Take the broken pot, and practice drilling on the remains. It is possible to drill hard plastic without shattering it. It takes patience, and you have to get a feel for it. Also, using a very thin drill bit helps. Once you have a small hole drilled, you can then move up to a larger drill bit on the same hole, and it'll go much easier. Just be patient with yourself.
I'm no handyman by any stretch of the imagination, but it can be done.