Hello
Attached is a scene that handles tight-fitting cloth, and also assumes the modeling scale is cm and not meters. I simply made two spheres. The inner sphere has radius 13 Maya units = 13 cm (assuming your scene-scale is cm). The outer sphere had radius 13.3, meaning there is a 0.3cm offset between the inner sphere (the collider) and the outer sphere (the cloth).
First of all - you must set the Scene Units to Meters parameter to map cm->m. That is of course 0.01 as 1 meter = 0.01 cm. (In your post, you say you set it to 0.1 which means MPM solver thought your scene was in decimeters, not centimeters).
In order for the MPM cloth solver to "see" that small difference of 0.3cm between the collider and the cloth, we must set the detail_size on the solver to be close to that number. The detail size is ALWAYS expressed in meters. So the default value of 0.15 is likely not going to work. In my example (attached) I used 0.05 - meaning the MPM solver will resolve simulation detail at 5cm (0.05m = 5cm). Now, 5cm is a lot bigger than 0.3cm, but it looks like it's enough to resolve the collisions without problem - even when animating the interior sphere. The general rule of thumb is to try to use as large a value as possible on detail_size, so just experiment to see. Perhaps even larger values will work; I did not try.
Anyway hopefully this helps! Just replace the cloth sphere, with the character's cloth geo, and the inner sphere, with your character's animated geo, and see if it works.
