FIRST: There is really no such thing as "permanent" thread locker (AKA Loctite). Basically, there are "medium-strength" (Blue) and "high-strength" (Red) thread lockers. Blue is intended to be replaceable with common hand tools. Red is sometimes called "permanent", but that only means that it usually requires heat to be applied first to weaken the bond before tools can be used to loosen. Let's assume you've used heat as well as penetrating oil.
I realize that your goal is to get that jamb nut loose so that it will then be free to screw IN or OUT so that the alignment shop can then adjust the toe in or toe out accordingly.
But you appear to be trying to loosen this nut by holding the INNER tie rod in place with one wrench while turning the jamb nut with another wrench to loosen. That is not the best way to accomplish this, as you are fighting both the thread locker and the years of corrosion on that threaded portion of the INNER tie rod as well as the bond where the INNER tie rod threads into the OUTER tie rod.
STEP 1: Unscrew the OUTER tie rod from the jamb nut:
Don't attempt to hold that INNER tie rod in place to loosen the jamb nut. Instead, put one wrench on the jam nut and another wrench on the OUTER tie rod. You SHOULD then be able to turn break that bond free and turn the jamb nut independently from the OUTER tie rod. The INNER tie rod should still be frozen to the jamb nut at this point.
Next, assuming the jamb nut (along with the INNER tie rod) will turn independently from the OUTER tie rod, back that jamb nut off a couple of turns from the OUTER tie rod (the INNER tie rod should still turn along with the jamb nut).
Once you have the jamb nut and INNER tie rod backed off a couple of turns from the OUTER tie rod, you're then ready to break that jamb nut free from the INNER tie rod.
STEP 2: Unscrew the jamb nut from the INNER tie rod:
For this step, you'll now put one wrench on the hex portion of the INNER tie rod and another wrench on the jamb nut. But now you're going to be turning these in the OPPOSITE direction from what you been doing so far. That jam nut should "unscrew" a bit from that INNER tie rod pretty easily now, since you're not fighting all the other variables.
Once you get that jam nut to move a bit on the threads of the INNER tie rod you can work it back and forth to chase the threads, applying penetrating oil as needed, until you've got that jamb nut moving freely enough to drop the car back off at the alignment shop (though I'd be leery of any alignment shop that can't break these components free in order to adjust toe).