So the home school is 7K but what WOULD you pay?
Room and board anywhere would be 11K a year, give or take a bit. The challenge is whether you have a pragmatic approach to the room and board cost or that is solidly built in to your price point. Nothing is going to beat 7K a yr because you are excluding living costs. Full rides are like hens teeth, maybe if her stats improve she could look e.g. Alabama or UT Dallas, but that is not necessarily offering a better school, just sleep away school.
Do you have any financial need?
Will your 4 year take her DE courses for core engineering? that might not be the case of OOS schools.