if potential tracking concerns you, put them in a faraday bag outside of work hours. The only situation where bringing multiple phones with you could hurt you would be a malware infection. Naturally, this is incredibly rare but not impossible. Have you looked into hardening your two work phones?
Generally, you should worry more about keeping personal activities separate from work activities. This situation is a lot better than doing work-related activities on a personal phone. This level of compartmentalization should be enough for most people.