Hi XXXXXXXXX,
I will answer your question about hair loss, but first I'd like to discuss with you some facts about trying to keep wild mice as pets.
Adopting wild mice and keeping them as pets is a very dangerous practice. For one thing, mice can carry diseases and some of those can be dangerous for you. They can carry rabies, which means that if you were bitten, you could require painful shots for a long period of time in order to survive!
Plus, wild captured mice do not do very well in captivity. It is far better for wild mice to be allowed to live as wild creatures by being placed in a safe area and set free.
Think of this: these mice had freedom and now they have been placed in some sort of cage. This might be compared to having your freedom removed and your having to live in a small room, unable to do the things you love to do, and with no way of understanding why this happened. The mice are simply not going to be happy about this situation. Mice purchased from quality sources have never known this freedom. But I do not expect your mice are going to adjust very well to captivity and, even if they survive, will not be happy as if they were free. If you want to have pet mice, it is far better to purchase some from a reputable pet shop or an individual you know whose mouse has produced babies.
Mice carry a bacteria called Mycoplasma. This bacteria can spread to other pets you may have. But, in the mice, the bacteria lives normally unless it multiplies to a greater than normal population and stress or illness can cause this flare up to occur. Catching a mouse and caging him is certainly stressful to the mouse, to say the very least. If the mycoplasm is not control -- which means a trip to the vet to get the right medication and right dosage -- then it can quickly kill the mouse. If you have other pets, such as birds, the bacteria can spread to them. I have had to rush my parrot to the vet because of mycoplasm before (not caused by mice, however) but the parrot got really sick and vet visit are expensive. So, if you have other pets, that is another concern. Dogs and cats can get it too.
During the 12th century thousands of people died because of the plague. This was a result of the fleas carried by mice and rats that were sick biting people! So, you see, taking wild creatures into the home really can be dangerous!
There are some places where it is actually illegal to capture native wildlife and keep it confised as a pet without a special permit. Those who have permits use them to help wildlife that require rescuing for one reason or another such as an animal that has been injured and can not live in the wild any longer.
Since the mouse losing hair and developing reddness around her bottom came in from the wild, it be easily caused by mites or another parasite. It be caused by lice which can spread to the other mice and even to you! There is a possibility it might be caused by a fungus growing on the skin. All of these can cause redness and hair loss. It might even be just scratching and rubbing itself due to the stress associated with being captured and confined. In order to get a proper diagnosis, the mice would need to be taken to a vet and treated based on the vet's advice.
I'd like to recommend that, if you love these wild mice and want really want to have mice as pets, let these wild creatures be free by releasing them in a safe area away from people and cats, and purchase some domestically bred mice (not brothers and sisters if you plan to cage them together in case they have babies or all of one gender if you want to ensure there are no babies in the future) that have never experienced total freedom. Domestically bred mice will be comfortable as pets, are usually pretty tame when you first get them, and are not likely to bring disease and parasites into your home since they have not been located in outdoors where these things are usually gotten, and domestically bred mice will love being a "pocket pet" for you after they have a little bit of time to get used to you. Pet mice are very reasonably inexpensive and even the fancier color mutations do not cost a great deal.
I'm including some links about pet mice to help you choose some good domestically bred pet mice and care for them properly. I do hope that you make the right choice about your mice. If I can help further, please use the "reply" button after accepting this answer.
Pet mice: http://exoticpets.about.com/cs/careofmice/a/mousecare.htm and http://animal-world.com/encyclo/critters/mouse/mouse.php
AFRMA General Care Page: www.afrma.org/rminfo1.htm
Pet Mouse FAQ: www.rmca.org/Resources/mouse-faq.txt
Fancy Mice: www.fancymice.info/
Diet: http://exoticpets.about.com/cs/careofmice/a/mousecare_3.htm
Care: http://www.hilltopanimalhospital.com/mice&rats.htm
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