If you are interested in engineering, your choice should be easier. There are many scholarships available for women engineers and admission is generally easier because of the lower number of applicants. I’d start by running the NPC on some of the better engineering schools to get a good idea of what it will cost.You will need a comprehensive list of your family assets and income to calculate it. Then start exploring scholarships including merit scholarships specifically for your target engineering schools. As an engineering student you also have higher earning potential as an intern during the summers.
Some OOS schools like Michigan, Ohio State, Michigan State, etc. give very good FA for desirable candidates. You may find that private colleges cost less than public because of better FA.
Another path is through the military, including ROTC or the service academies. Navy ROTC is particularly attractive for engineers.
You can go to law school after engineering. You will be qualified for more technical law areas (like IP) with an engineering background.