i firstly want to say that i have never violet gobies myself, but i did do some research a while back, so i'll give you something to start off with until someone more qualified adds more.
they are brackish. i am actually going to look at what wetwebmedia says on this subject right now... ok the article i was reading said 0.005-0.010 http://www.wetwebmedia.com/ca/volume_3/cav3i3/Dragon_Gobies/DragonGobiesart.htm
salt water is about 0.023 for comparison. as the article suggested ocean salt wouldf be best, this goes for any brackish setup.
i was going to mention a few other things, such as the need for sand substrate, but the article seemed to have covered it better then i ever could. i would however highly recommend aquatrol20 spirulina pellets though. they can be taken whole if the fish likes, otherwise they break apart nicely into the sand for substrate sifters.
anyway, wetwebmedia is a great source of info. everyone who contributes on that site is usually a published author or in some way an authority in their field so i probably cant add anything to the care that wasn't already covered so instead i'll address the redness you mentioned. i couldn't quite tell if a bacteria was suggested by your description, but adding a fairly high level of salt as you will probably be doing anyway will probably take care of the problem. if you want though, you could add a little melafix to be safe without causing any harm.
these fish are absolutely not suited for "pet store" conditions and are very lucky your mom made an impulse purchase. not that im saying impulse purchases are good ideas, lol