If you get a chance, get some video taken of your skiing, post it on youtube and link it here. This way we can tell you for sure what is going on.
If you're going to ski hard all day, you should be tired at the end of the day, but you should be tired all over. 99% of the students I teach that complain of specific muscle tiredness either have gear issues or technique issues (mostly technique). Most of these skiers can reduce or eliminate the tiredness problem far easier through technique change than through fitness improvement. As you've deduced, the most common cause of thigh burn is sitting back. Two common reasons why you could be sitting back are vertical movement with no ankle movement and lack of forward movement of the core.
Here's an exercise you can do at home that might help: sitting in a chair. First try to sit so that your back fits flush with the back of the chair when your butt makes contact with the seat. Do you notice how your belly button moves backward as you sit? Now stand up (and move the belly button forward). Without moving your feet try to sit so that your butt is on the edge of the seat by sinking down slowly. Did your heels come up off the floor? See how your belly button hardly moves backward at all? You should also notice that you have to bend your ankles to make this happen in the second sit and that your ankles do not bend on the first sit. Now try that second edge sit again, but this time stop before your ankle comes up off the floor (don't go all the way to a sitting position). From this "squatting" position, try to stand up again, but try to stand on your toes as soon as you can. Notice the "forward" movement of the belly button this time? Try this again doing the same movement, except for lifting the heels off the floor. Feel the weight shift to the balls of your feet? I'll call this movement a "squat-forward" move.
When you start a turn, as your skis start pointing down the fall line, they will start to move faster than you are moving. Think what would happen if you were on skis on flat ground and someone laying on the snow pushed your boots forward from behind you. If you were prepared for it, you'd stiffen against the push and everything would move together. If you weren't prepared, your feet would move ahead of you and your belly button would move backward like you were going to sit in a chair and you'd either fall or recover and pull yourself back up. In a ski turn, you can't stiffen against the push from gravity if you don't use your ankles. You have to move your core (e.g. the belly button) to avoid sitting back. If you are trying to recover from sitting back all day (even just a little), you are going to be doing a lot more work. Compare thousands of "sits" to thousands of "squat-forwards". The timing here is subtle and critical, but the more time you spend "sitting", the faster your thighs are going to start burning.
One of the ways we can make turns on skis is to straighten the legs to release the old edges, flow the body over the skis to the inside of the new turn, then bend the legs to sink weight down and engage the new edges to go in the new direction. If that last step is down without ankle movement, you're getting in and out of the chair on every turn. The least you can do is to turn the chair sit into a squat-forward. But if you can add turn types where both legs bend to start the turn and then finish the turn with both legs extending or turns where the new inside leg bends while the new outside leg straightens, then you will have a much bigger tool kit to deal with different terrain and snow conditions. Using the best tool for the job can also be a lot easier on the thighs.
So whether you are sitting at the end of your turns to engage your new edges or simply failing to move with the skis as they begin accelerating down the hill, the solution is the same: use your ankles! When you get that problem fixed, your next leap forward in skiing will be using your ankles differently. If this does not solve your problem, then the next step is video or an in person lesson with a pro.