Hmmm, 2 is pretty little for entertaining herself for several hours, I would think. Honestly, I would probably resort to movies on a laptop, computer games, or a tablet. I bring my 8 year old to work often, I am a massage therapist, so while I'm with clients she hangs out in the office. She is able to read, do artwork, look through seek-and-find books, etc., and have limited screens. I really despise screens for such little ones, especially before age 5 or so, but if you have no other choices, I would think that'd be the most entertaining thing for your girl?
I agree with pp that your boss might not be as cool with it as they seem to be. My mother runs an office and told her office manager she could bring her child occasionally, but the employer took it a different way and is being too lax about it. Maybe check in again and make sure you're all still on the same page.