Whether the secondary trustee (often called the "successor trustee") can change the distribution of trust assets after the two original trustees are gone depends on the terms of the trust
document. I assume that you are talking about a living trust. Normally, a successor trustee has no authority to change the the distribution of a living trust's assets after the trust creators, who are also the original trustees, have passed. Normally, again, once both trust creators are gone, the living trust becomes irrevocable and none of its terms can be altered.
A living trust can be created that gives the successor trustee authority to change the trust's distribution provisions. But as I've said, this is rarely done. Certainly you don't want that.
A question I have here is why you are concerned that your successor trustee might try to alter the distribution provisions of your trust. You want to name as your successor trustee a person you completely trust and can fully rely on. If your current successor trustee isn't that person, I suggest you name someone who is as successor trustee. If there's no one you completely trust who can serve as successor trustee, I suggest you take other actions to insure that your desires for your trust property are carried out. You could give a copy of the trust to several major beneficiaries, so each would know what the trust requires. Or you could name a co-successor trustee, to watch your original choice and make sure that the distribution is done right. You shouldn't have to worry that your desires for your trust property could be changed or negated by your successor trustee.