Bismihi ta'ala
From a shar'i perspective, it would depend on if she meets the requirements for a shar'i legitimate marriage.
However, this approach such a husband takes is definitely inappropriate and morally wrong, especially among all things breaking a promise.
If the husband is that uncomfortable in his first marriage, he should not drag her into the humiliation of lies and deception to fulfill his needs, and should be honest and straightforward with her.
And Allah knows best