William Finch and Edward Terry, two British visitors at Jahangir’s court heard the rumours that there was a lady named Anarkali, who was wife of Akbar and mother of Prince Daniyal. He and Jahangir had a love affair while Akbar was alive and when he got to know about it, he confined her alive in a closed wall and she died.
No contemporary sources of Akbar and Jahangir mentions Anarkali, Neither Akbarnama or Tuzuk-i-Jahangiri. Other scholars also does not mention any such incident.
If there was indeed such a woman, she might had been a concubine/courtesan because Salim would not dare to have an affair with Akbar's legitimate wife. And if she were a Concubine, how could she say no to a prince. He might would have secretly punished her as her voice didn't matter.
Altogether, there might be some truth behind the rumours but again, no literally or archeological evidences are available to prove the legend as truth.
Anarkali Bagh also does not mention Jahangir or salim and therefore has no evidence for it to be belonging to real Anarkali.
Her being mother of Prince Daniyal is pure rumour and isn't supported by legitimate sources at all.