Can you buy big round bales of decent grass hay?  IMO your filly is underweight and has a wormy belly.  I use Ivermectin Gold or Quest Plus 2X/year and then I rotate Ivermectin/Panacur/Safeguard every 2 months.  If my horses aren't responding to the routine de-worming schedule I use a Power Pac or 2X the Fenbendazole dose for 5 days in a row.  That usually takes care of any hangers on.  
I feed my Arabians the Daily recommended amount of Purina Omolene 400 feed and they have free choice grass hay while out on pasture.  Right now pasture is kind of a euphemism, so they get a big round bale of hay to eat on.   I'm using Omolene 400 because it's what seems to work best for my horses, I don't care if you prefer Nutrena Safe Choice or Atwood's Brand 12% feed or oats or corn chops or whatever, just FEED that baby.   
Your filly is only 2 years old and growing, she's going to need lots of calories for that.  If she's already thin going IN to winter, she will be a RAIL coming out in the spring.  I've been there, I've done it, I've seen how skinny a horse I THOUGHT was being well fed can get.   I've raised horses on straight alfalfa, now I'm on straight grass because I can't feed the local alfalfa due to blisterbeetles.  Probably not an issue where you are.   My horses don't do worth SPIT on nothing but grass and I have every age from 7 months all the way to 28 years old now.  I just put my 32 yo horse down last week because of his arthritis, otherwise he was totally healthy.  
At one point I had 14 head of horses and I spent over $1000/month on feed.  Arabians are NOT generally easy keepers.  Some are easier than others, but my friends who have Quarters feed less than 1/2 of what I feed and their horses are porkers.   To get and keep a young horse in prime shape, not necessarily show shape, you need to feed some concentrates plus a minimum of 25 lbs hay, free choice per day.  Notice I said minimum.  If you have 100 lb bales of grass hay, I'd set one out for her to eat and see how much she eats in 2 days time.  I'm betting at first she'll eat that hay up like a Hoover and then once she's getting enough she'll slow down to appx 1 bale every 3 or 4 days.  Leave it free choice so she can graze and feed her the concentrates 2X/day.  She'll fill out, calm down and become much easier to get along with.  
As for finding a trainer, I too do not recommend most Arabian specialty trainers.  BTDT too, sat down talked to them discussed what was expected, got the ya-ya and went up and found weighted, dang near big lick shoes on my HUNTER for God's sake.  Brought him home and he will be going to a local hunter/dressage trainer who is fairly close so I can check up on whether it's lipservice or for real what they tell me.   I would go hang out at a local open show and see whose horses are well behaved, quiet and respectful and that's where I'd start.  Go spend a day at the trainer's barn and just shadow them all day.  Stay out of the way, don't ask a lot of questions, just watch.  If you can get someone to come out to your place, that's awesome, but for your safety and the filly's, she needs to have some training very soon.  
The only thing I'll address is her 'neck snaking' thing.  If she's getting fed enough, she'll quit.  She's trying to dominate you into dropping her food because she's hungry.  I make my horses stand and face me and give me 'Pretty Ears' or I move on down the line to the next horse and the horse with the ugly ears or who presents their butt doesn't get their concentrates til next meal.  It only takes one or 2 missed meals and they quit with the disrespectful behavior.  So if she snakes her neck, rears or anything you don't like, walk away and take the food with you.  
		
		
	
	
  Lucky, 32 yo horse I just put down
  Peppermint Patti, Res Champ Pinto Mare
  svs Il Divo, 2 y.o. Jackpot Colt, Arabian Sport Horse Nationals, he placed 3rd, would have been Reserve Nat'l Champ if I'd been able to get a little more weight/muscle on his hip/butt area. 
  svs Viado, he's a little rounder than I'd like, but he's going into saddle training within the next 30 days and he'll shape up quickly. 
  Patti & Hillbilly Harley DCA at 6 weeks 
I didn't put these up to brag, but so you can see that my horses are very well fed and in pretty decent shape.  I show regularly and I show from babies to senior horses.  I'm not saying a word about the fencing, as you can see we're still re-fencing our place.  We have that horrible hog wire that was topped with barbed wire & Tposts too.  I have covered all of the Tposts and have replaced the barbed wire with electric tape.  Slowly but surely, we're replacing all of it with wood posts and top rail with no climb mesh and a hot tape inside the fence line to keep the beavers off the top rail.