Okay, I tried this out and I think I get what is supposed to happen. You said the pattern says,
Insert right needle into next 2 sts at same time as if to K tog and transfer to LEFT needle, slip same 2 sts one at a time back to LEFT needle, k1 through back loop, p1.
I think this is incorrect. Either you or they made a mistake here. It can’t say LEFT in both of those places. What I think it should say is :
Insert right needle into next 2 sts at same time as if to K tog and transfer to RIGHT needle, slip same 2 sts one at a time back to LEFT needle, k1 through back loop, p1.
You insert the right needle into the next two stitches as though you were going to knit them together, but just slip them over to the right needle. At this point the two stitches have switched positions. To maintain that “twist” you now move them back to the left hand needle just moving the left needle point straight into the stitches, needle point to needle point. Now the two stitches are back on the left hand needle and ready to be worked . Now knit the stitch nearest the left needle tip through the back loop, then purl the next stitch. Now you’re finished with that twist and ready to move on.
The left twist is given as:
Slip next 2 sts one at a time as if to K, insert left needle right to left through sme 2 sts at same time and transfer back to left needle, p1, k1.
This is written correctly. Slip the next stitch knitwise, then the following stitch knitwise as well. Now they are both on the right hand needle. This next part is an unusual maneuver and feels a bit weird. Move the left needle into the second stitch from the tip of the right hand needle from right to left, and on through the first stitch at the same time, (You could think of that left needle as moving into the stitches purlwise if that makes better sense to you. But remember that this is a very non-standard movement for knitting and both needle tips will be pointing off to the left as you are doing this step.) and transfer them to the left hand needle, ready to be worked. These two stitches have now exchanged places, or been twisted, which is what you want. Purl the first stitch and knit the second one. Now the left twist is complete.
Of course, you will need to make sure your yarn is in front whenever you are purling and in the back when you are knitting.
I tried this out, purling back after I did a row with each of the twists. Then I put another row with the twists one stitch over and did that for several rows and got what you said, a vertical line with slanted lines of branches coming off of it. So I think it works. If I have not made something clear give a holler and I’ll try again.