Ring patterns of concentric 2pi solitons in molecular orientation form in freely suspended chiral smectic-C films in response to an in-plane rotating electric field. We present measurements of the driven dynamics of ring formation under conditions of synchronous winding and of the zero-field relaxation of ring patterns, and propose a simple model which enables their quantitative description in low polarization DOBAMBC. In smectic-C*A TFMHPOBC we observe an odd-even layer number effect, with odd layer number films exhibiting order of magnitude slower relaxation rates than even layer films. We show that this rate difference is due to a much larger spontaneous polarization in odd layer number films.