More healthy food if the other issues have been addressed, as you say, and I know ,trust me : I have twins in my Family it isnt easy,if It is a food issue , let them eat , make sure its healthy stuff fill the fridge with veg and Dip and fruit and crackers and goodies, most of our 'real" goodies are actually healthy,let them make some of their own food , jello is a delight, I love it, they would love to make their own, also Parefait is so easy to make. They need to be busy aswell fill up their lives, make their heads spin with activities.Give them projects with small rewards for completing them, trust me think it out They are challenging My Daughter has a quiet one and a 'Rowdy"one they are identical and on a light note I still get in trouble for not being able to tell them apart.
Everything you mention I do. When there father when he has the day off is with them. Thats all I give them is healthy food. They rarely gets sweets. We have a set up or stations for them to do different things like color, paint, and play board games, we even break them up to help with cleaning dishes and help cooking. I am always supervisioning them but I also have school work and job and another daughter, who also needs my attention. Where we leave the only time they get to go to the park is in the summer too cold for them to go out in the cold they have asthma and get sick easily. They are also in gymnastics to burn off that extra energy. Like I said we have tried everything.
I think your girls need more supervision they wouldnt be able to do the things you state in your post if you were around them, also maybe more activities to keep them busy, does Dad play with them do you all go to the local parks for fun and games, they sound bored and that will make them look for trouble ,give them more positive attention and you will get better behavior, as they are looking for food and you say they are skinny, feed them more, give them good bowls of Cereal in the morning and a bananas or Yoghort, Soup and bread for lunch,Fruit,... Spagetti, Rice , fish sticks, carrotts and apples.