Okay, here is how I think you do it.
Left mitt: The first 2 needles will be the back of the hand and the last 2 needles will be the palm of the hand. Back of hand will be worked first over the 23 chart stitches and then the palm comes next knitting every row.
Set up round will be: P1, k8, p5, k8, p1, k21. (On the first mitt you did the palm first now you do the back first so you do the set up for the chart [back of hand] then do the 21 palm stitches.)
Work 2 repeats of the chart just like for the other side and read the chart from right to left all the time just like you did before, working the chart at the beginning of the rounds instead of the last half as before.
Next round: Work the 23 stitches following the chart then knit across the palm stitches until you have 8 remaining. Using waste yarn, K6, slip these sts back to the left needle and knit them again using the working yarn, K2. Continue normally until you have worked a total of 5 repeats of the chart.
The pattern says this next:
Rearrange the sts again for the rib: 12 sts on the 1st, 2nd and 3rd needle and 8 sts on the 4th needle.
Work [K2, P2] rib for 4 rounds. BO all sts.
I think that should work just like it did on the other mitt. If you doubt it do it backwards: 8 on the 1st, 12 on the 2nd, 3rd, and 4th.
The thumb will be just like the other one.