You are asking "how I can show doublesided display" but if i'm understanding your problem correctly what you need is to not show double sided faces.
To do that open the Viewport Shading menu and put a check against Backface Culling.
Edited to add:
You appear to have a set up something like in the screen shot below:
View from below and the teath in my "snake head" are hidden (no Backface Culling):
With Backface Culling enabled teath are visible :
and finally Vieport Display > In Front unchecked:
another edit :
Perhaps for the inside where the In Front option is causing problems, disactivate that and use a Offset distance in the Shrinkrwap modifier to keep the faces above the high poly model as in the image below.
......... or simply assign the outside faces to a vertex group for ease of selecting/deselecting and hide them while working on the iside if the snakes head.