First off, I'm so sorry your sister went through that and I hope she has had some form of counselling/therapy to help her cope with the PTSD.
On to your question. I'm fairly sure tattooing anyone under 18 falls under a charge of assault of a minor. Also, how good is the fake ID really going to be? Any reputable studio should know how to check an ID and one that doesn't probably isn't a good studio.
Your sister may look older but at 16 I doubt she looks older than maybe 21/22. Every studio I've ever been tattooed in checks ID, even if you look old enough. I get checked and I'm 38. My friend is the artist in a studio and they still ask me for ID so they can say they have checked it.
The repercussions on the establishment could be anything from a fine to being shut down and that wouldn't be decided by you so I'm not sure how you would ensure no repercussions for them.
Basically, you're being totally unreasonable.
A life plan at 16, I had one of them too. It's not an indication of maturity or anything. It's just what we do as teens to start thinking about our lives when we're out of school and in the world. A boyfriend, again, loads of 16 year old have those. They usually last a few months to a year and then they bugger off to uni in different cities and forget each other's names. Again, not an indicator of anything other than normal growing up.
Oh, but in case you do decide to try this anyway the artist won't be asking you where she should get it done so if she says her forearm or somewhere you have decided is restricted, that's where it's going. And it'll look highly suspicious and weird if you're like "no, no, sis, remember we talked about this and you've not to get it there."