Hi lnov,
Welcome to the Mattress Forum! 
I’m sorry your mattress isn’t working out as well for you as you would have liked, but at least you did have the foresight to purchase something with a good exchange/return policy. You didn’t mention which Alexander model (Hybrid or Signature) or which comfort designation you chose, so I can’t comment on this as compared to the other new mattress you’ve chosen.
As you’re probably aware, Quality Sleep Shop is a member here and I think highly of their knowledge and componentry.
It is quite common for a new mattress to be firmer than the showroom model. There will be a break in period as the mattress loses any of its “false firmness” and the cover stretches and loosens a little and your body gets used to a sleeping surface that is different from what it is used to (see post #3 here ). This would typically be a few weeks but it can be shorter or longer depending on the specifics of the person and the mattress.
While it’s not possible to “diagnose” mattress comfort issues on a forum with any certainty because they can be very complex and there are too many unique unknowns, variables, and complexities involved that can affect how each person sleeps on a mattress in terms of “comfort”, firmness, and PPP or any “symptoms” they experience … there is more about the most common symptoms that people may experience when they sleep on a mattress and the most likely (although not the only) reasons for them in post #2 here, post #6 here and post #3 here.
Using my “theory at a distance” goggles, what you’re describing would be typical of a mattress that has a surface comfort that is too firm and doesn’t allow for enough of a “cradle” when sleeping on your side. Being too firm, the hips and shoulders would bear most of the weight and there would be a lateral curve in the lumbar/lower thoracic region. While these areas would still be in contact with the mattress, again the “stretching” from the lateral curve and lack of cradling with to firm of a surface comfort could create and uncomfortable total side surface sensation. Also your comments about a bit more comfort being achieved with only 1" of latex (unknown type and ILD) would “generally” lead to the conclusion of too firm of a surface comfort as well. But this is of course a guess.
So you really don’t sleep on your side, but half rotated, with characteristics of a prone and side sleeper combined. Discomfort in the outer thigh area, (I’m guessing on the leg that is in contact with the mattress) often comes from two issues. First is when the hips sink in too deeply into the mattress, stretching the tensor fascia latae/iliotibial band complex, especially if this is tight, which is common among both active and inactive individuals. The second common cause of this pain is when a mattress is a bit too firm on the surface, and with the added weight of the upper leg upon the lower leg that is in contact with the bed and effectively “pressing” it into the mattress, this can create discomfort for not providing enough pressure distribution. I can’t speak to the Alexander mattress, as I mentioned earlier I don’t know the configuration and model you had. You can see if you think either of these two scenarios make logical sense in your particular situation.
Regarding temperature, the Emily uses a pocketed spring unit with 1" of 1.8 lb. polyfoam, 1" of 14 ILD latex (I don’t know if it is Dunlop or Talalay) and 1" of 1.5 lb. polyfoam in the quilt. All of these foams tend to be quite breathable materials. In very general terms … the materials, layers, and components of a sleeping system that are closer to your skin will have a bigger effect on airflow, moisture transport, and temperature regulation than materials, layers, and components that are further away from your skin and softer mattresses or foam toppers will tend to be more “insulating” and for some people can sleep warmer than firmer versions of the same material.
There is more about the many variables that can affect the sleeping temperature of a mattress or sleeping system in post #2 here that can help you choose the types of materials and components that are most likely to keep you in a comfortable temperature range. Also, your mattress pad/protector can also dramatically affect mattress surface comfort.
Hotel mattresses in general tend to be on the “firmer” end of the spectrum, and then using top of bed products added plushness is achieved. These products of course have a breaking in period, but unless you were in a hotel with a new mattress on one side of the room and an older one on the other side, you wouldn’t be able to recognize this. When a hotel mattress feels better than your mattress at home, it’s usually a sign that your current mattress is worn out, as opposed to the high quality or appropriateness of the hotel mattress for use every night at home (most of which would be a poor choice due to their lower quality componentry that most of them use due to their frequent need to be changed out).
It could be a possibility that you still have a bit of “learned alignment” of sinking in from your old mattress, but after two months away that normally would be the case. Everything you seem to be describing with your current mattress “seems” to be pointing at something that is too firm on the surface. There is a 60 day comfort guarantee with Quality Sleep Shop, so you do have some time to analyze the product and see if it gets better. In the meantime, you may wish to contact them and let them know that the topper they sent made a bit of difference but you still think that you need a bit more plushness and see if they would send you out a thicker piece to experiment with.
I’ll look forward to your progress and feedback and you go through your process.
Phoenix