You leave her in there for TWO HOURS?! If I found out someone was doing that to my child, I would raise holy hell.
If you have so many kids and are so busy that you can't work with this child, then please, simply tell the parents it's not working out.
What you're doing is just cruel. Would you do that if it was your own child?! Of course not! Don't try to justify it by 'the parents say she's happier than ever'... she's happy to get the heck out of there!
Ask the parents what her schedule is like at home, and adhere to that. It's not fair of you to ask a 1 year old to go by YOUR schedule just because it works for everyone else. Every child is different. If she needs to nap at a different time, go by that, don't make up new rules that a 1 year old doesn't understand.
ETA: Big deal if you change her, the issue here is SLEEP. You're letting the crib babysit and you're concerned more with your quiet time than the well being of the child, There's clearly an underlying issue here, which you're ignoring by leaving her in there for 2 hours. Why is she going to the bathroom so much in 2 hours? I don't remember any of my kids having BMs during nap time after infancy.
You completely ignored what I said: You're not going by the CHILD'S NORMAL SCHEDULE, you're going by what suites YOU, and it's clearly not working. It's not about you, it's about the child. You get paid to take care of the child... so take care of her. I've clearly hit a nerve here: the innocent don't feel the need to defend themselves.
If it's not working out with this kid, just tell the parents. It's not the first time in the history of the world it's happened; no big deal. You're not happy, the kid's not happy while she's there, end the professional relationship. And maybe she doesn't need to sleep (and definitely not for 2 hours!!)... my son is 21 months and takes about one 30 minute nap a day. Give this kid a break. Leaving her in a crib for 2 hours is just cruel. You can't remember what the mom said about naps on the weekends... ASK HER! That's your job!! Just because you haven't 'let go of a high needs child' doesn't mean that you shouldn't, doesn't mean it's not the right thing to do.
Don't single me out just because you didn't like my opinion on it. If that was my child, you'd be out of a job.