I agree with using a one rein stop, but I would first teach her how to do one. (I think it's more effective that way) To do a proper one rein stop, you take your hand and clamp it to the side of your hip, and you do not let go until she releases the pressure. (make sure your other hand is forward so you're only pulling from one side) She will probably walk/spin in a circle for a while, stand still, pull against your hand, poke her nose up, down, etc, and finally start licking and chewing, and release the pressure. Immediately release the rein as soon as she releases! And only then. Practice this on both sides several times every day. Eventually as soon as you bring your hand to your hip she'll stop. Then when you really need to use the one rein stop (like when she's trying to drag you) she'll stop.
When she drags you to the gate, does she point her nose towards it first? Does she start drifting her shoulder towards it? Does she give you any tiny clue before she heads out? Most likely she does! Watch for any signs (even a flick of an ear) so you can get her moving past the gate (cut off that section of the arena if you need to). When she starts going to the gate, point her nose away from it and kick her forward, using a crop if you need to.
Most of all, she needs to learn that leaving the arena does NOT mean her work is done! On barn sour horses, I spend literally hours going out the arena, to the barn, back to the arena, to the barn, etc. Sometimes I get off, tie them up in the barn for a 5 minutes, and then get back on. Sometimes I walk to the barn and trot away, over and over again. (never let her go faster then a walk towards) On really barn sour horses I ONLY leave the arena by backing out of it (make them work for it! And it's harder for them to bolt out). Sometimes I get off at the arena, walk down to the barn, and then give them a good lunge in front of the barn. No matter where she is if you say work, she works! If she bolts back to the barn it is very important to WORK HER BUTT OFF! Never ever ever just get off and untack!
So, this post is a bit of a novel... but I work primarily with ponies and wow, do I get a LOT of barn sour guys in! It might take a while (esp if she's been doing this a while) but keep mixing it up, work her butt off all over the place and eventually she'll get better and better.