From what you write, I'm not sure who has moved in besides your sister. At any rate, the confusion is the kind that so often happens in families. You think she is living in your unit as a temporary guest. She thinks it is a business arrangement - lodging in trade for child care!
It would be helpful if you and your husband have definite plans, complete with time line, for the unit she's living in. But I don't know any way you can "evict" her (that may well be her take on it) and not hurt her feelings. She may get angry no matter how you try to do it.
But you (hopefully you both!) need to make it clear that you meant your invitation to be only for a few days, that you have other plans for your house, and that she will have to find a permanent place to stay elsewhere. Give a date by which she must remove herself. Expect a reaction!
In addition, keep in mind that if you were not absolutely clear in the first place - which, again, easily happens when you're trying to be kind to a relative - then you will have to apologize for misleading her.