On one level, the bunny boiling incident seems like pointless cruelty from a dangerous stalker. If you think about it though, there may be a deeper meaning involved. Initially, Dan is against buying a rabbit, and his wife and daughter are for it. So when Dan spontaneously buys the rabbit — after betraying his family — it may be a guilt offering. Dan is expressing regret over his affair, and wishing to re-dedicate himself to his family. For Alex, this is literally gut-wrenching. Dan regrets ever being with her! When she attacks the bunny, she is symbolically attacking Dan's love for Beth and Ellen.
There's also the so-called "rabbit test", a 1930's pregnancy test that involved rabbits being injected with a woman's urine. The rabbit would then be dissected several days later to inspect the rabbit's ovaries for changes indicating that the woman was pregnant. Alex killing the rabbit doesn't just mean that she's trying to destroy Dan's love for his family, she's also simultaneously reminding him—again—that she's carrying his child.
Alex could have hurt or even killed Ellen had she wanted to.
Good thing they took the dog with them when they went to visit Beth's parents, or she might have killed him too.
For animal lovers, imagine that poor bunny's final moments. It has no idea what's going on or why, all it knows is that this strange woman took it from it's cage, put it in water and now it's in such pain. And it probably wasn't instantaneous either.