Why is my filter unstable and self-oscillating in this case?
The question is not very specific so this will also be just a general answer.

The stability of a composite linear-time-invariant (LTI) system composed of smaller LTI systems cannot be deduced from the stability of the component systems if the composition introduces feedback. Instead, you should test the stability of the full composite system. The system is stable if the poles of the transfer function lie inside the $z$-plane unit circle. So write out the transfer function of the component systems and also the transfer function of the composite system in terms of the component transfer functions. Find the poles of the transfer function of the composite system. Write an inequality that is the stability condition, and you may be able to solve from that an inequality for the acceptable values of a system parameter of interest, in terms other parameters.