Is it OK to CoolSculpt my inner thighs in the same week that I Emsculpt my Quads and Hamstrings? And will fatloss be permanent?

You can have the treatments done the same week, but not in the same area. Coolsculpting does not actually remove fat, so fat loss is not permanent. Coolsculpting does cause some scarring around areas of fat to encourage the fat cells to shrink. This does not always work or work well. Liposuction is much better to remove fat and the fat cells removed are gone, however, this does not prevent weight gain.

I think you’re going to find that none of these treatments are going to improve skin laxity of the inner thigh.
Ask your provider about timing.
From my perspective the timing is irrelevant because the treatment choice is incorrect.
Sorry to come across as pessimistic or blunt. Best,
Mats Hagström MD