The formation and control of m-fold symmetric vorticity hole structures in a two-dimensional vortex patch with a line vortex core is studied within an adiabatic contour dynamics theory. The holes are formed by subjecting an initially circular vortex patch to an m-fold symmetric, oscillating, chirped frequency straining flow. The theory uses adiabatic invariants associated with the boundaries of the patch and describes all stages of evolution in the driven system, i.e., the emergence of the m-fold symmetric V-state, resonant passage through the boundary of the V-state, formation of vorticity holes, and autoresonant dynamics of the driven holes inside the vortex structure. The results of the theory are in a good agreement with the fast multipole-type simulations. In contrast to free (unstrained) m-fold symmetric vorticity hole structures, where only m = 1 case is stable, resonantly driven phase-locked m>1 vorticity holes can be stabilized by the external strain. More complex, stable m-fold symmetric vorticity structures with local minima in vorticity distributions can be formed from initially axisymmetric distributions by external, chirped frequency strains.