So I a made a script that lets the player grab a vertex, move it, and then update the mesh. To help prevent the player from trying to clip it through other objects I made it so the mesh/collider is constantly being updated. It works however there is an issue where it keeps falling into itself. So I tried updating the constraints to prevent this but it doesn't seem to help anything.
With the mesh being updated after the LMB is released: http://gifyu.com/images/withnocollisionprevetnion.gif (SE doesn't like non-imgur links apparently and they are too big for imgur).
With the mesh being updated in real time: http://gifyu.com/images/withcollisionprevetnion.gif
Also here is a gif showing how constraints on the RB don't solve the problem (I've tried freezing on different axes but those still cause issues too): http://gifyu.com/images/constprob.gif
So basically what can I do to prevent the object from moving when it's mesh/collider is being updated?