Let them see certain of the documents. See the list of pages to take to the bank, in the instructions included with the trust. Bring copies of each of those documents on the list to the institution at which you wish to open the account. Don't bring any other parts of the trust, even if they ask for them. If they are not satisfied with the items on the list, then thank them politely and go to a different institution.
If the institution at which you are applying is at a significant distance from you, then you could fax or email the documents. If you can physically visit the institution, then simply walk in and bring the papers. Ask any questions you wish to ask, but the main request is to have their legal department or trust department look over the papers you have brought and tell you whether they would be happy to open an account for that trust. They may have some questions they wish to ask you. It is usually nice to politely provide the answers, if the questions are reasonable.
As to credit unions in the USA and their equivalents in other countries, we have found in the USA that they are willing to open the account only if the signatory's credit rating is at a certain level -- we believe it was in the 600s. Since they are a credit union, they care more about the credit score of the personal signatory than they do about the structure of the trust or what kind of laws it is based on. The same kind of priority might exist at equivalent institutions in other countries as well.