does she have a electric wheel chair or motorized scooter? if so she could take them on that no problems!
imo the reason the chihuahuas cry when taken away from her is becuase #1 they are nervous and #2 they have control over your mom so they feel powerful with her its there comfortzone they dont want to leave it.
does she have a treadmill? she could put the dogs on the treadmill everyday dogs are usually fearful at first but once they get comfortable with it they usually love it.
im sure im going to be critisized for my methods of dog training here i like useing a combonation of cesar millan and posative re-enforcment (in otherwords firm but happyily)
if you dont like this thats fine not many people do you either agree with cesar millan or you dont thats fine perhapes youll get someone else with a method more to your likeing.
but if you should wish this is what i would do for the chihuahuas around other dogs
keep them on lead around the other dogs ti will probably be easier to do one at a time. i am guessing that these dogs dont allow other dogs to come close to them and stand back to bark am i right? they will be a few feet away from the other dogs and bark then when the otehr dog comes near or turns its back then it attempts to bite?
in this situation i would imedietly pick the dog up turn it around holdign it tight and call the the other dogs over to sniff its bumm hell struggle his gorlw maybe even try to bite at the other dog but dont let him dont let him go untill hes a bit calmer not barking or struggling when you let him go when ever he attempts to bark or growl give him a quick jerk on the lead and a make sure he feels it dont be afraid to jerk a little hard obviously not so hard that you fling him across the yard lol but hard enough that he feel its and good be firm dont put up with his crap tell him "NO" when you jerk and jerk him EVERYTIME he growls or bark little throaty growl barely audible jerk him and say NO.
once he understands that your taking control and not going to allow him to do this he may try to hide with the lead dont let him walk him around the yard if you come close to a dog and he growls or bark stop,jerk and scold him. some dogs get the message and ry to attempt meeting or sniffing hte other dog go ahead and let him but the second he growls or barks or snaps jerk him tell him "no" and scold him.
in this type of situation some people would say to use treats everytime he is good persoanlly i dont think thats a good idea as the reason the dog is barking or growling at the other dogs is becuase its showing dominance or attempting to when you bring food into the mix they feel the need to protect it and could cause the aggression to become worse. same with toys some dogs protect there toys. and dont think "well my dog has never ha food agggression" well they dont have to but any dog will guard its food from another dog they have too if they didnt the other dog WILL take its nature if you are not going to prove to me you want it badly enough im going to take it from you. i never worry about about a dog growling at toher dogs who get around the food bowl ti does not mean they have food aggression it just means the other dog is trying take the food from them. IF however another dog is obviously not showing signs of wantingto take the food away and the other dog attacks then that is cuase for concern.
but im getting ahead of myself thats not your problem is it
like i said before if this is method does not make you feel comfortable if you read it over and think ehhh i dont like the sound of that thats fine theres always moe then one way to train a dog i ish you luck!