Can I take kids with just a written and signed agreement (even notarized)?

Mother gets one hour supervised visits per week. My son is 7 and my daughter is 5. They both want (truly want) as do I to move. I have primary custody. I'm trying to figure this out because I’m now evicted for letting her stay with me. I have 1 month to get out and already have a place to rent in another state but mediation will take too long to schedule. The mother is bouncing around from places to stay. Is there a quick action to take to get court approval? Is there a way where she thinks I'm going for a limited time and then switch the files to make her have to come up to when I start a custody adjustment up? I'm not trying to be mean but the kids want to go with me and I even tried offering her the summer.