Usually we want family to visit....but this sibling, I don't think he should be around mom. She wants to ask him to come from out of state, to come and take whatever furniture & household items he wants. That of itself is not a bad idea, except I fear that while he visits, he will take mom to change her Will, maybe drive her over to her bank and encourage her to change beneficiary to be himself, things like that. Since I am the DPOA and Executor I don't want his charming influences over mom. He hardly ever visits--years go by--so when mom talks of inviting him, I think she really just misses him terribly. And she confuses missing him, and being overjoyed with seeing him, and tries to reward him by giving him money, and (I fear) changing her important documents. It sounds irrational, I know. But how do I guard against her making an irrational decision?
The real issue is not keeping him away, but keeping him from exploiting Mom. As DPOA you need to be involved in all legal transactions so make it clear that you will go along if they go to a lawyer or the bank, etc.
But if Mom is still competent to make her own decisions, she can change her will or insurance beneficiaries or give away cash. If she is competent, she can do what she wants with her possessions. Your presence may help her make reasonable decisions but you cannot really prevent her from doing what she wants with her estate.
And your Mom could even hand your brother his box now if he starts asking about things, tell him that Mom put together a box of wonderful items that she thought he would like to have.
As for your brother taking your Mom out, tell your brother that Mom feels more secure if you go along with her.