This is a pattern for simple toddler-size children's mittens made with double-pointed needles in-the-round. The "three dots" difficulty is only because some people find working the thumb with dpns to be fussy. If you know how to knit in-the-round, you really CAN make a pair of mittens for your 2 year-old.
I used sock-weight yarn for this project. I love Stonehedge Fiber Mill fun mill ends and they were perfect for this project. It is good to use something with animal fiber such as wool to help maintain natural body temperature. My kids can't wear synthetic fibers, which is why I went with the Fun Mill Ends, which are an extremely soft mix of sheep wool, alpaca, and llama.
I knit wool baby items and sell them at www.etsy.com/marcyartsy if you would like to see my handiwork.
7 stitches per inch for stockinette in-the-round.
100 yards of Fingering weight