In the USA, you normally only need to send 3 letters of recommendation:

1. One of them should be your dissertation supervisor (if diss < 5 years old)
2. One should be a current supervisor (such as your new postdoc advisor)
3. One should be from a committee member or someone else who knows your work well

As long as you have three, I think you're fine in not including a letter from the  postdoc advisor that you're having problems with.

**tl;dr:** Letters of recommendation are used to indicate that **some** (at least three) faculty think highly of you, not necessarily that **all** do.