I find the Frankfurt examples (and other examples in the same style) to be a useful way of illustrating that the Principle of Alternative Possibilities is false (see the first section of this video discussing the topic for an introduction and the remainder for a more detailed discussion). In the following I've tried to provide a concise capsule on the relation of the examples to the larger argument. My examples are derivative of Frankfurt's but not exactly the same.
In summary, the Principle of Alternative Possibilities is based on our moral intuition that coercion lessens or removes moral responsibility of a moral agent. Thus, for example, if a bank employee is credibly threatened with death if they do not help a bank robber, we generally do not think that the bank employee is morally responsible for their role in the robbery. Why? We generally say it is because they were not acting freely in the situation. They were under compulsion.
First Example - Aligned Threat
Supposed that a disgruntled bank employee (Jones) was planning to burn down the bank because of their mistreatment of him. However, when Jones arrived at the bank parking lot, he was confronted by a man wearing a V for Vendetta mask (V) who told Jones that unless Jones burned down the bank, V would kill Jones.
In practice, of course, this seems like a very unlikely scenario, and very hard to prove. However, suppose it happened. Would Jones now be inexcusable or less responsible? It seems that he should still be responsible: he was doing what he wanted to, and V's threat didn't affect anything.
Some would respond, though, that the responsibility was because Jones' choice preceded the threat and was a free choice in the sense that Jones could have chosen otherwise.
Second Example - Will Endorsement/Removal
It's harder to imagine a circumstance where Jones' will could be bypassed. However, suppose that V had taken a different tack. Suppose that V entered the scene earlier, before Jones decided whether or not to burn down the bank, and was able to anticipate what Jones would decide, and could prevent Jones from deciding not to burn down the bank. Seeing that Jones would decide to burn down the bank without any interference from V, V simply does nothing, although V would have stopped Jones from deciding not to burn down the bank. In this case, it is hard to see how Jones is not responsible, even though Jones did not have access to an alternative possibility.
The typical responses to this are:
1) There is no way for V to anticipate what Jones would do, because that information does not yet exist (assuming indeterminism is true).
2) There is no way for V to make Jones decide to burn down the bank, because a decision is only a decision if it is free.
As to (1), if God can know the truth of future contingents of creaturely freedom and can communicate them to V, then there is a way for V to anticipate what Jones would do.
As to (2), all that's necessary to remove the power of alternative possibility is to render the alternative impossible.
A sur-response might be that V is not rendering the alternative impossible but only incompossible with V's plans.
As to this sur-response, however, since the preceding state includes V's plans, a defense of possibility here requires possibility in a sense that divides out a causal contributor.
While compatibilists can speak of such things, it's unclear how one is arguing for incompatiblism while at the same time dividing out even one causal contributor.
It seems better to understand coercion in terms of causal contribution to the actual result. For example, if the otherwise loyal bank teller would not have robbed the bank, then teller is excusable. On the other hand, the disgruntled Jones is not off the hook just because he did what V wanted him to do. The compatibilist interpretation of the anticipation situation acknowledges that decisions can be anticipated, and thus easily says that Jones is fully responsible even without any alternative possibility because the lack of alternative possibility (in the sense suggested in the example) is irrelevant as it exerted no causal influence on Jones.
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