In my experience with acclimating tree monitors, I have found that water is the most important part of their acclimation. Freshly imported tree monitors are skinny because they are dehydrated, not because they are in need of a meal. Monitors, as with many other reptiles can go months without food. It is water that is so very precious to them. Unfortunately, I see so many keepers set their tree monitors up in aquaria, with a screen top. This is probably the worst type of situation you could give a tree monitor. Tree monitors come from tropical indonesian forests, whree humidity levels virtually never drop below 60%. So, you must keep these high humidity levels in your enclosure. If you are using an aquarium type setup, instead of using screening as a cover, cover the top with plexiglass, which will trap in moisture. As for a substrate, use dampened sphagnum moss. It is also important that you give them adequate heat. Do not let the ambient air temperature drop below 85 degrees, and offer them a basking site temperature of at least 130-140F. Mist them several times a day, and keep note if they begin to drink the droplets of water. If you notice they are still not drinking, I would suggest givieng them daily soaks in warm water. HYDRATION IS THE KEY. DO NOT HANDLE or constanly peek into their enclosure, as this will only stress them out, and will only worsen matters. I would suggest that you separate the two, so that you can closely monitor each one's progress separtely. You should also cover up the viewing glass of their enclosures as they acclimate so that they are not stressed out when somebody walks past their enclosure. Once they begin to start drinking on their own, you can start to attempt to feed them. Use mouse pinks,fuzzies and rat pinks at first. Just place them in an open area where they are likely to be found. If you have corrected the humidity/moisture problem, and adequate heat is given, the animals should come around.
In all honesty,(not directed at you) it is unfortunate that so many people jump into tree monitor ownership, without the necessary skills to properly acclimate them. Many people think that you just slap them in an aquarium as you may with a savanah or a nile, and they'll do fine. However, tree monitors are probably one of the most skittish reptiles, who have proven to be one of the most difficult animals to acclimate to life in captivity. It is inexperienced keepers who do not know what they are doing, that lead to the high mortality rate of these beautiful animals. Unfortunately, most distributors and importers do not acclimate them, or properly care for them, so when the hobbyist buys the animal, it is in even worser shape than when it first came in.
As far as vets go, I would make sure that I take them to a vet who has adequate experience and knowledge working with reptiles, not one of these vets who claim they deal with "exotics". For, an inexperienced vet will administer the wrong, harmful drugs to your animals, or ultimately misdiagnose an illness altogether. IT is important who you choose to use.
But, I hope this information helps; I have used these techniques to acclimate several black tree monitors and blue tree monitors. You must keep in mind that humidity and moisture is the key to their success; you must try everything to keep as much moisture in the cage(I would shoot for 85-90%humidity). You must also make sure that they start drinking on their own. Many tree dwelling reptiles do not know how to use a waterbowl, for being arboreal, they very infrequently encounter an area of standing water. They usually drink water droplets off of the surroundings during/after rainfall. I wish you the best of luck with your new captives, and let us know how it goes. Take care, have a great day.
Bob-

The Odatriad