You may or may not have the right to read the trust document. If you are a named beneficiary, once he passes away the trustee is obligated to give you a copy of the trust so that you know what your rights are. Then you read it (and/or hire an attorney to read and explain).
If you have a copy of the trust, or if you get one in the future, it will have specific sections for what happens [a] when the first spouse dies, and [b] when the second spouse dies. Even if you don't have any rights until after the second spouse dies, I believe you will have a right to a copy of the trust once the first spouse dies (assuming of course that you are a named beneficiary). But if you aren't, such as "100% goes to XYZ Charity when the last one dies", then I doubt you have any right to read the trust. If that were the case, I'd still advise the trustee to give you a copy . . . if nothing else, to get you off his/her back and so that you aren't suspicious and that you have clarity as to your father's wishes.