I absolutely will let her get her license. I have no problem with it. After she's had it for a while and has been out with my dad and brother I'll consider letting her try our car. I wouldn't feel comfortable with her driving it while she's brand new to driving though.
Do your dad and brother live with you? Because it's a bit inconvenient for someone to get good driving experience, and a lot of it, if the only car they are permitted to drive is not easily available. When my daughter was learning, she learned and got her hours by driving my husband and I everywhere. Whenever we went somewhere, she drove. What kind of car do you have that you are so certain a 17 year old can't handle it?