How is Penelope’s reaction to the beggar different from the reaction of her suitors?
I assume that your question refers to Penelope's reaction to Odysseus disguised as a beggar, since there are other beggars in the palace, and one in particular, Iros, plays a part in the scene you need to analyze.
The scene in question is Book XVIII in Homer's The Odyssey. It angers Penelope that someone she has taken under her roof is ill-treated and scoffed by her unwanted guests. Unaware that the newly arrived beggar is her own husband, she has offered him shelter and food, and will not have him humiliated. She is about to reprove the suitors about their behavior when Athene enwraps her in sleep.
In the meantime, the suitors enjoy themselves by making Odysseus and Iros fight between them. Iros loses, but Eurymachus begins to insult "the beggar" whose identity will soon be disclosed by saying that begging is much easier than doing an honest day's work. Odysseus replies that, if given the opportunity, he will outdo Eurymachus at any task he proposes. The suitor, infuriated at the beggar's cheek, throws a footstool at Odysseus, who dodges it and someone else gets hurt.
Notice that Homer removes Penelope from this scene before she has the opportunity to establish her authority. This is probably because the scene is a piece of dramatic irony in which the suitors make fun of the man that will take their lives.
When Odysseus defeats Iros, they mockingly toast to the winner:
May Zeus, stranger, and all the other immortals give you
what you want most of all and what is dear to your spirit,
for having stopped the wandering of this greedy creature
in our neighborhood.
In fact, little do they know that what he wants most is to punish them for their misdeeds and that, to Odysseus, they are the "greedy creatures" in his neighborhood, that is to say, correlatives of Iros.