The trick to the utkatasana while facing the side is the same as the earlier twisting subroutines. Press firmly into the mat with the opposite foot to the direction your twisting, so if your turning to the right press the left foot firmly into the mat as you lower into your squat, it does seem to make a difference.
In the Ashtanga system the entry to pasasana is a standard utkatasana, facing ahead but I find this twist to the side before squatting in Vinyasa Krama, helpful in setting up for the bind.
Another approach I came upon by accident is to turn to the side and then do a full forward bend, hands to the mat, before squatting into the sideways-on utkatasana, this makes a interesting exit from the posture too. This wasn't how Ramaswami taught me but it's a nice option if you struggle with a sideways utkatasana and benefit from the added support of your hands on the mat.
The bind is very tricky, you need a secure and comfortable utkatasana and good flexibility in twisting.
This posture took me a year or so to grab my fingertips without using a belt to work my hands together or a rolled up towel beneath my heels.
Here are some tips and hints that might make it come a little more quickly than it did for me.
Focus on your breath and give some thought to bandhas to help anchor you. you can do it without them but they'll probably make it a lot easier.
As in the first picture below, twist as far to the right as you can and stretch your arm out and as far back as possible.
Dip down bringing your shoulder in line with and preferably below the knee ( pic 2)
Keep leaning out to the side almost to the point of falling over as you start to bring your arm around and press your shoulder and knee against each other to give you more stability (pic 3)
Rotate the palm out and over as you begin to reach back, think trying to put on a coat that has the sleeves tangled (pic 4).
This one I find key. Try and bring your forearm up as high up your left leg as possible, right up on the knee (pic 5). It seems too high but as you'll see in the next picture (pic 6) the knee will bring the arm down as you begin to bind.
Now you want to shift the pressing together from the left arm/right leg to the left arm/left leg which will keep your secure as you begin to reach your other arm around. It's not really pressing together but rather your pushing your knee down against your arm which is in turn pulling up against the knee (pic 6 still).
Nicely secure and locked in place with the left arm and right knee, begin the twist by bringing your right shoulder up and around while sliding your arm firmly down your back towards your waiting hand (pic 7).
At first you'll settle for fingertips. If you hold a scarf or belt in your right hand you might be able to swing that towards your waiting left hand and get some sort of bind that way, shuffling your hands down the belt a little further each time until your clap fingertips (pic 8)
Eventually, with practice, you'll be able to keep twisting, I find it's a twisting and lifting up out of the pelvis that helps take your shoulder even further around and allowing a deeper bind at the wrist.
I'm sure there are many other approaches but this is the one that currently works for me.
In the video you'll see that on the second side, due to the sweat, my arm slips a little off the knee. I'm still getting the bind but really only one knee. Drying your knees and shoulder helps, some put a cloth over their knees but on a good day I find I'm able to get the full bind around both knees and on the sweatiest of days, it depends how flexible and warmed up your are that particular morning.