The best option that clarifies the antecedents while maintaining coherence is:
C. Enrico had to work from home and take care of his two-year-old son. Enrico planned to make a call to his co-worker Paul while they walked over to the park. Enrico, helping his son on the playground slide, talked to Paul using a hands-free headset.
This option removes any ambiguity by clearly identifying who is helping whom and who is being talked to during the call.