a = (dot(v, w) - p*div(w) - div(v)*q)*dx + 0.5*dot(v+grad(p),w+grad(q))*dx L = f*q*dx
if that's what you're asking
Taylor hood is unstable for darcy, no? In which case it's not surprising it breaks.
For you VMS formulation do you not also have to incorporate a piece in the RHS? Also, the formulations I have seen have opposite signs on the velocity trial and test functions in the stabilisation term. But I'm only passingly familiar, so take these comments with a pinch of salt.