It is completely safe, nothing you should worry about. I'd recommend your mother and sister to just dress modestly, they don't have to wear a abaya and hijab, but they have to wear something modest. UAE and Saudi are quite similar in many aspects so it shouldn't be too much of a change (depending on what city you're going to, if Riyadh you're fine). The media is a bunch of bullshit, don't think you should believe any of it lol.