Hate is such a strong word, of course (how's "abhor?"). But let's face it: sometimes your fellow-Mommy soul mate comes attached with the child of your nightmares. How is it that a woman who is so cool, and seems to agree with so many of your parenting philosophies, has a kid so diametrically opposed to yours (or so you'd like to believe?) You love hanging out with her, but you don't know how much more of her child you can take. Here's what to do before smoke starts pouring from your ears:
1) Civility, civility, civility. Be careful not to let your frustration get the best of you. Don't let yourself treat her child with anything less than warmth and kindness-- not only would that be hypocritical, but it will only bring out worse behavior.
2) Seek perspective. Are you sure you're not being unduly harsh on the child? Might you just have seen him or her during some bad moments? If her kid always seems to conflict with yours, are you sure your child isn't contributing to it? Do you tend to have a negative judgment of a lot of different children, maybe seeing them in a harsher light than you do your own?
3) Brainstorm. Are there circumstances where the kid's behavior isn't as bad, or when your patience is a bit higher? Exploit those. Can you start focusing more on seeing your friend without either of your children? Are there activities you can suggest or outings you can plan that will help the kids get along better? Get specific in what you do--and what you avoid--to try to maximize the peace.
4) Get some space. If your frustration reaches the point where you grit your teeth every time little Jacob enters the room, or you reflexively become a human shield every time he comes near your child (who's gotten socked a dozen times already), it's time to take a break for your own sanity. Perhaps some time apart will help your kids get along better as well.
5) Be honest: sort of. It does no one any favors to keep your lip completely zipped if you think there are substantial behavior issues in your friend's child. It's not fair to the child, who might need an outsider's perspective and help, and it's not fair to your friend, who may not know that she's losing friends--and not doing right by her child--because of it. So, fess up that you sometimes find it difficult to hang out with her because of X, Y, and Z. Be specific, be gentle, and be apologetic, and support her in coming up with solutions. Admit your own vulnerabilities, and make it clear how much you like your friend and like her child (even if must cross your fingers for the latter.)
6) Prioritize. If no improvement seems to come, or the kid conflict has spilled into a conflict among you and your friend, it's time to make choices about what you're willing to accept. This might involve letting a friendship fade to keep your child from misery. A sad sacrifice, but not the first--or last--you'll make as a Mom.