Come, Kate, thou art perfect in lying down: come, quick, quick, that I may lay my head in thy lap. (3.1.19)
In the previous passage, we pointed out that Hotspur has an aversion to being intimate with his wife, especially when he's got war on the brain. So, why does Hotspur here insist that Kate sit down so he can put his head in her lap? Good question. Here's how we see things. It's not until Hotspur sees Mortimer with his head in Lady Mortimer's lap (as the Welsh woman sings a song) that Hotspur wants in on the fun. In fact, he demands that his wife, Kate, sing a song too. This seems to suggest that Hotspur wants to use his wife as a way to compete with another man, Mortimer. Hotspur could care less about getting cozy with Kate and he makes it clear throughout the play that he doesn't particularly care to hear her speak. (Feel free to disagree here.) For men like Hotspur, wives are kind of like trophies, tools used to make husbands seem more important.