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.

In my field 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.

Note: Some programs require more. Even if n number of letters are required, there is no requirement that the n be comprehensive.

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