if you go to another shop, they will probably charge you a full hour's work which in some areas could mean $75-100.
so the $50 is not a bad deal as a continuation for the work...but the part about them lying to you about this 'part' they need, that is not settling well with me.
they could've just told you they miscalculated the labor and asked you nicely if you can help out with the $50.