It is my understanding that an asset protection trust cannot allow the beneficiary to specify where the money goes after the beneficiary dies. That is, it cannot give the beneficiary a general power of appointment after the beneficiary dies. That is the trust must irrevocable specify where the money goes after the beneficiary dies. Am I right about this?
You are wrong about this.
An irrevocable asset protection trust can (and often does) contain a "special power of appointment" that a beneficiary can exercise.
A special power of appointment is a right to say who gets trust assets that forbids the person using it to distribute to themselves, their creditors, their estate, or the creditors of their estate.
In the real world, there must also be a showing that the special power of appointment can't be used (or at least, will not be used) in a way that circumvents these limitations as part of a larger plan (e.g. by making a distribution to a spouse who tacitly agrees to use the money to pay the power of appointment holder's creditors, or if two parallel beneficiaries use their powers of appointment to make parallel distributions to each other).
Some special powers of appointment are open ended, others have limitations.
For example, a power of appointment allowing someone to decide which charity trust assets go to at their death would be common.
Powers of appointment allowing the holder to decide who among the grantor/settlor's descendants gets the trust assets, in what amounts, on what terms, would also be common.