Hmmm ... it is odd to me how little dogs tend to be more aggressive than bigger ones to our rather "dominant" boy, and chihuahuas are noted to be among the top ten aggressive dogs. I am not sure exactly sure why this is, although the small dog may be scared underneath or gets some false bravado from his or her protective human.
In your shoes I would take them both out for a walk on lead and be very firm every time there is aggression on either side. As far as your mom is concerned, she has basically to want to like your dog, or at least make the effort. It is easy enough to get on with virtually any dog, in my view. You just take the time to try and be with the dog, do nice things with it (giving treats, stroking the dog where it likes - our boy likes a stroke on his chest or under his chin or a bootie rub). If your mom did that (in the absence of her chihuahua eg you could walk the chi for an hour) perhaps eg sitting down on the floor with your dog, hopefully things should start to come right.