As someone who struggles to balance life and work yourself, I think it would make the most sense to work it out with someone struggling to do the same.
Only pay her for the hours she actually works- start doing that by having a conversation with her about all this. Tell her what your issues are and that she is only going to be paid for what she actually does. And then tell her that the chronic lateness and absences must stop. Then you can institute a warning system from that point on. This is what is considered fair and air-tight in HR circles as well. If you don't have it in writing, she can sue and and quite possibly win. Best to do the right thing- ethically and legally.