You absolutely should look into internships for after your sophomore year. You might even be able to get one after your first year, if you want to try for one.
It's entirely possible that, if you're not taking classes over the summer, your dad will let you work. So that may also be an option, as you suggested. Talk to him to clarify. This could give you the spending money you want, without interfering with your studies, so it may be a good compromise.
It's not a bad thing not to work during college, so long as you have some sort of paid work experience in your history. Some employers only hire people who've held paid jobs, no matter how menial you think those jobs were, so it's good to have them. But they don't need to have been during college. Jobs in HS can be fine. Summer jobs now are fine.
It's okay to work during college, but most advisors say you really don't want to work more than about 10-15 hours per week. More than that tends to interfere with your studies. But if your dad really doesn't want you to work for now, don't work. Use that time for your studies, for extra curriculars, maybe do some volunteer work once a week or a couple times a month. If you don't work, and you get great grades, you can talk to your dad about this again.