Hang old buddy, sounds like it's time for you and Hairball to play "Incredible Journey."
Drive cat 30-40 miles out into the country, put cat outside of car, drive away.
This gives the animal a sporting chance, and is nothing like the old "burlap-bag-in-a-lake" trick.
Some domestic cats love a feral existence.
Then move. If the cat for some reason does make it back a la Disney, it's going to be really, really pissed.
This way you can say to everyone that the cat must have got away while you were moving, and you're really, really broken up about it, and you just don't know what to do.
Unfortunately, your new landlord doesn't allow pets, or you'd get another one so that your daughter and ex would have a cat to play with in the few and far between times that they might see you, but your hands are tied.
Every now and then, remember to look off into the distance wistfully, and look like you might start to cry. When your daughter or ex says, "What's wrong dear?", you just look down at the ground and say, "Oh nothing...just thinking about 'ol Hairball...never knew how much that old cat really meant to me..."
I've been trying for a few years to figure out a way to get rid of "Muffy", but my family is too smart, and has caught me before.
"Where are you taking the cat?"
"Um...nowhere hee-hee, must have left the window down on the car. Just getting her out..."
I feel your pain.
Mk