Lightly defrost chicken in microwave to separate them
What you have done is fine. Not only are you not facing a safety issue, but because you didn't allow the piece that was to be refrozen to completely thaw, you're unlikely to even face the quality issues that refreezing poultry often sees. (Refreezing poultry tends to play a bit of havoc with the texture)

One small thing...our grandmothers rinsed chicken. It has been definitively shown that rinsing chicken (purchased from a reputable store) is unnecessary, and may actually do more harm than good because it doesn't significantly reduce pathogens on the surface of the chicken, but it will spread those pathogens (if present) around your kitchen.

Related: Cooking, freezing, recooking, and refreezing chicken