tamte

only position and orient is updated from the pinned points when Match Animation is on

if you want to update the pinning itself you need to do it within the solver, for example this are the changes I did to your file:
- renamed group2 to pin, no functional reason, just for readability
- set pin type to stopped (this is not really necessary as assigning i@stopped inside of the solver will do the same, but I left it like that)
- in the solver add POP Wrangle or Geometry Wrangle, set Input 2 to First Context geo :
- decreased the Bend Stiffness and Thickness just so that they bend nicely

Houdini Apprentice can't export Alembic, so that may be there reason, unless you have Education version which also produces hipnc files, which should be able to export .abc
https://www.sidefx.com/products/compare/ [www.sidefx.com]

only Hair can have true orient related constraint, even though you are not taking advantage of that in your file as you are pinning 2 root points instead of 1

however to get your left side working the way you may expect with 2 segments attached
- turn on Tangent Stiffness on /obj/VELL/vellumattach1
- increase your Bend Stiffness on /obj/VELL/vellumcloth1 to something like 1x10 or more
(or to 1x0.01 but also increase solver Substeps to 3)