UUI comes from the originator of the call leg. If you want Communication Manager to copy through UUI from the first call leg you must use the consultation call API method to initiate the second call (which you say you are doing). Also you will need to ensure that any trunking that is involved is configured to carry UUI data. There are FAQs that cover how to check this on Communication Manager.
Assuming that trunking is not involved and that UUI was present in the first call's messaging,
to troubleshoot further I would first enable TSAPI tracing on AES and look more closely at what is happening in the messaging from CM to AES relative to UUI. There is a DevConnect FAQ covering how to enable and access TSAPI g3trace information. https://www.devconnectprogram.com/site/global/products_resources/avaya_aura_application_enablement_services/support/faq/tsapi/index.gsp#10
UUI is also dependent on the negotiated protocol version between the application and AES, and the configured Switch Connection ASAI link version on AES.
Deep analysis by the devconnect team of the logs or system configuration would require a DevConnect Support Enabled membership.