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You need to file in the state where you have resided for at least the past 6 months. You can go to Illinois, and still file in Nebraska.
However, if your husband is not agreeable to you having the children, then he can request temporary custody of them and you will be forced to bring them to him. I suggest, it is best to file and get everything done before trying to leave the state unless you feel he will not care enough and you can establish residence in Illinois of 6 months and then file there.
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