Liangmin,
Put it this way - even if you don't get along with your CL, at least after 1 mth she will be gone. Furthermore, she is your employee, if you feel she is not good you can always dismiss her early or at least tell her off. It's not so easy to do with one's MIL.
I also think that even if a CL is costly, you don't feel so bad about making her stay up at night tending to the baby, etc since after all you are paying her to do it. If it is MIL doing a lot of extra work, your dependence on her and what you 'owe' her may put a strain on your relationship. You will also feel like you should go along with her suggestions on how to take care of baby even if you don't agree with her, out of respect. Guess it depends on how well you get along with her.
I agree about not wanting to do confinement at ILs place, it's more about the comfort and privacy. 3mths is a long time to spend there. Also, have you already decided that MIL and maid will be primary caretakers of your baby after you go back to work? There's nothing wrong with the arrangement, except maybe to consider that after the baby arrives, your feelings about this arrangement may change, but by that time it's hard to 'reverse' the decision and tell MIL that you rather have the baby stay at your place, etc.