To answer your question, you need to read the provisions of the family trust carefully to see if there is an express prohibition against securing your interests in the family trust as the trust's beneficiary for a loan. If the trust precludes what you want to do, then you cannot obtain a third party loan using your interest in the family trust as one of its benficiaries as collateral for the loan.
If there is no prohibition for such in the trust, you should still advise the trustee of you desires and obtain written permission before proceeding. A problem is that the lender will want to see the provisions of the trust before any loan is made. Beneficiaries under the trust as well as the trustee may not like the idea of a copy of the trust being provided to any lender.
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