Katherine was brave and helpful and J.J. was wily and quick. We chased the rodent back and forth across the back of the house for about 10 minutes, all while I explained why we didn't want the mouse to get into the house. We finally got it to go through the lawn, which slowed it down enough so that I could whack it with the kids' baseball bat. 

I think I was yelling "AAAAACCKKK" and Katherine was crying at that point. The poor little guy didn't have much chance and there it lay, still and silent...dead in our lawn. Grace came over and stomped on it (I think she was imitating my "I must protect us against this evil invader" instinct). Then she said, "Oh Mommy, why did you kill Kathleen?"
"Kathleen?!?" I thought. We hunted this animal, killed it, and now you're naming it? J.J. piped in, "Can we keep it?" I quickly replied, "Yes, we'll keep it in the garden, buried under my lilies."
And why Kathleen? Grace comes up with the weirdest names for her stuffed animals - she's got a puppy named Avillary, a buffalo named Moose whose brothers are all named Balooka, a giraffe named Giffidia . So why does the lifeless little fuzzy lump get named Kathleen? There must be some psychological significance, right? Who knows what goes through the mind of my 4 year old!