The idea of reducing the algorithm is that if you can show that the Hamiltonian Path problem can be solved using the constrained MST problem, (with a polynomial time reduction), then any polynomial time solution to the MST problem would allow you to solve the Hamiltonian Path problem in polynomial time. As this is impossible, it would prove the constrained MST problem cannot be solved in polynomial time.
What you are trying to do is the opposite - proving that the Hamiltonian Path problem is at least as hard as the constrained MST problem.
Note that you stated in the comments that your assignment was to reduce from the Hamiltonian Path problem, and in the question you said you were trying to reduce to the Hamiltonian Path problem.
You can easily solve the Hamiltonian Path problem using the constrained MST problem, as a Hamiltonian Path will always be a spanning tree with 2 (or 0 for a Hamiltonian Cycle) leaves.