Yes, step one is separating your 2 Beardies, she's
black bearding and not eating because there is a dominant/submissive thing going on. Not only are they housed together but it's a tank that is too small, and they have no UVB. If you don't separate them ASAP you're going to come home to a badly injured, or named, or dead beardie or Beardies. And the reason her back legs are paralyzed is because she has no UVB lighting, so she is not processing her calcium or vitamin D3, and most likely has MBD. If she was on sand she may also be impacted, when is the last time she had a bowel movement?
I'm sorry but you need to buy 2 adequately sized enclosures immediately, separate them, and then have 2 bright white basking bulbs and 2 long florescent tube UVB lights, only Reptisun 10.0 tubes or Arcadia 12% tubes. If you're in the US then the Reptisun 10.0 is readily available, and much cheaper online. I think the 18" inch 10.0 tube at Petco costs $38 x 2, plus you'll need to buy 2 18" fluorescent tube fixtures at Walmart (cheapest place, they have them for $10 a piece), but if you order the Reptisun 10.0 18" tubes online at
www.petmountain.com they are like $20 or so a piece. So petmountain.com is the cheapest place for the bulbs, and Walmart for the fixtures. Any bright white halogen bulb can be used as a basking bulb, you just have to judge what wattage based on what size the tanks will be, and you'll need to spend $10 x 2 for 2 digital thermometers with probes on wires at Petco. That's the only way to accurately measure their cool side, hot side, and basking spot temperatures, which will also effect their digestion if the temperatures are off. Also, you'll need to be dusting all of their live insects in a calcium powder with vitamin D3 5 times a week, and also a Multivitamin powder 2-3 times a week. It's a lot at first, especially for 2 dragons, but as you can see if you don't do things properly they get very sick and eventually die.
If you cannot afford to buy 2 enclosures and 2 of everything else, my suggestion is to find a reptile rescue and surrender one of the dragons immediately, because you already have one that is seriously sick. It's not your fault, pets shouldn't be gifts, especially if the person giving them buys the wrong stuff for them. But at this point you need to act quickly because the paralysis may not be reversible, and she will soon stop eating completely, plus the other dragon that is healthier and no doubt larger is going to hurt or kill her...