Kindly remember a few posts ago, where I showed several versions of mock hairpin lace. There is no "right" way, but rather one should choose the best version for the project at hand.
This is the way I came up with that works best for my angels. You can see the traditional crocheted hairpin lace on the left and the tatted mock lace on the right.
The basic idea is split rings like this: 2 -- 1 -- 1 -- 2 / 2 -- 1 -- 1 -- 2 clr. Of course, the first and last in a strip of lace may be regular rings instead of split rings. Depending on the pattern, there may be 3 or 4 long picots on each side. I haven't tried it yet with smaller or larger numbers of picots. Instead of the 2 ds at the beginning and end of each ring, I tried 1 vsp 1 and 1 + 1, joining to the previous ring, but this proved to be too fiddly to be worth it.
With the blue angel, I carefully gave each picot a half twist just like real HPL when I made the joins. The result originally was sort of lanky and stringy, but I was able to block it to look nice.
With the white angel, I joined to the long picots keeping them straight with no twisting, and got this pretty effect without the need to block. This is a little like my broomstick picots.
In both cases, when joining to the long picots, I was careful not to pull the join too tight, which would bend the curve on the loops.
If you want to know more about broomstick picots, named for their resemblance to broomstick lace, see my post HERE, and there are more patterns using that technique in my book "Playing with Picots"