Can a wife have a trust, living will without her husband in it?

Yes and no.

So yes, if you have a prenup.

If you don't have a prenup and you get a will or a trust without your husband, then they can do something called an elective share.

And this is for the wife or the husband.

If you disinherit your wife or your husband, that wife or husband can claim a certain share of your estate, even if they were not mentioned in the will or in the trust.

There might be other types of trust, like irrevocable trust, asset protection trust, that you may be able to keep it out of your husband's hands but for the most part if you're trying to do that type of setup, I think it makes sense to have it in line or in congruence with a prenuptial agreement.