Having a tattoo on your eyelids should not preclude you from using and enjoying the benefits of Latisse. I recommend that you follow the directions of the manufacture (apply at bedtime to each upper eyelid daily) and you should see results within 6 -8 weeks.
A single episode of Latisse into the eye will not damage your eye. There have been rare reported cases of darkening of the iris with prolonged use. THis drug was actually used for glaucoma and the noted side effect was longer eyelashes and that is how it came to be a cosmetic treatment.
Latisse is approved by the FDA for patients ages 18 years and older. Since your daughter is 15, technically she is not able to receive the treatment. I would suggest waiting until the recommended age to undergo Latisse.