I see. How about then making simplify() call doit() on Subs()

>>> simplify(x0*Derivative(f(x0, y0), y0) - x0*Subs(Derivative(f(x0, _xi_2), 
>>> _xi_2), (_xi_2,), (y0,)))
nothing changes


>>> (x0*Derivative(f(x0, y0), y0) - x0*Subs(Derivative(f(x0, _xi_2), _xi_2), 
>>> (_xi_2,), (y0,))).doit()
returns 0 as it should

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