To what extent is it permissible to say, "All praise is due to You, there is nothing better than what You have decreed, but my heart is utterly broken," and does this constitute an objection to divine decree and destiny?

The statement "my heart is broken," if intended to express sadness, is a natural human feeling that one is not obligated to suppress and for which one does not incur sin. Rather, one should not express discontent but instead speak good. The Prophet, peace and blessings be upon him, grieved at the departure of his son Ibrahim and said: "Indeed, the eyes shed tears, and the heart grieves, but we do not say except what pleases our Lord." Sadness can even be an indication that the heart is not hardened. What is forbidden is to express discontent with Allah's decree.