In such a small tank, your problems are probably caused by poor water quality. I would try and get the larger tank up and running as soon as possible. I would put the gravel from the two gallon tank into the 30 gallon to try and "seed" the tank with as much good bacteria as possible. Also, I would put the 2 gallons of water in the big tank, too. It isn't much, however, it will at least contain some good bacteria. What you could do is put the little fish in a bucket with the two gallons of water, then take out the gravel and put that in your new tank. Fill the tank, and add whatever decorations and such you are going to use, hook up the filter and let it run with the filter going until the temperature in the new tank matches the temperature in the bucket. This will all be stressful on your little fish, however, I think the 30 gallons of water, even if it is unseasoned water will be better than the two gallons of poor water.
For a hospital, quarantine tank I would suggest a minimum of 5 gallons. The little two gallon tank would make a nice home for a little betta
Also, in the hospital/quarantine tank, I would suggest a foam filter that could be cleaned and dried after treating a sick fish, rather than an undergravel filter. Fish medications often kill the good bacteria in a tank, so it is best to have a filter that can have new media put into it after a disease has been treated. Also, a bare bottom tank is easier to deal with as a hospital tank.
I think that you will notice a huge difference in your fish when they have more water. Toxic substances such as ammonia and nitrite which are deadly to fish build up very quickly in a small tank.
I hope this helps, and if you have any questions, please do not hesitate to ask. We all have been at the stage you are at now, and we are all learning together