Basically, I have two classes that share a bunch of such internal functions (no object required, it's just string parsing)

Put the functions into a third, non-class module, export them, and use it in both your class modules.

Inheritance only works for methods, not plain ol' functions. And inheriting from a class that you've no intention of using inheritance--just so you can import some functions that live in the same file--leaves you open to all kinds of nasty surprises down the line.