I am sick of my housecarl. What is the easiest way to get rid of her? (besides killing her myself)

Besides dismissing her?

You could always have them join the Blades.

you can dismiss her?! Thank you sir.

you can dismiss the Bard.

But Stewards and Housecarls are bound to your residence until Death, or they join the blades

how do you get her to join the blades?

One word: Boethiah.

That's a name, not a word.

Very much this^^!

OP said she doesn't want to kill her though

The easiest one word is...

disable

Why do people think that is an absolute requirement to do the Blades quests? It actually isn't if you don't wait. I've always done them as soon as I get into Sky Haven Temple (after 'Alduin's Wall'), and also refused to do that in the end.

welll you could just take them on a trip into the wilderness and then fus ro dah them off a cliff

EDIT: If you don't want to kill them only option i know off is the blades.

op doesn't want to kill them though

Next time you'll decide to visit the central tundra, bring her with you. Don't forget to pull a mammoth's tail whilst screaming along the way.

Aside from turning them over to the Blades, I dont really see any other way other than killing them.

ok thanks. I guess we are going to take a walk in the woods....

Why exactly would anyone want to get rid of their housecarls anyway? They protect your property while you're gone, after all.

I can understand being annoyed by what they say, but their usefulness outweighs everything else.