As a fellow Chihuahua owner I have to say I'm am
very distressed to read that your Chihuahua is not allowed inside. These are inside dogs, they were never meant to live outside.
Toilet training is all part of dog ownership. It takes time and you have to put up with a few puddles on the carpet (and yes that can take months and months to correct...but you do it because that's the responsibility you've taken on). She makes a mess because you let her, you have to teach her not to. She is a dog...doesn't speak our language and has no concept of right or wrong.
Sorry, I know I sound harsh but I just love these little dogs so much.
Here are a few things you can do, since your mum isn't getting any aggression from her I'll assume your mum cares for her.
Get your mum to stop taking responsibility for her and start to divide up the care between the whole household, particularly you and your siblings. You (all children in the house) should feed her (and she shouldn't be free fed).
Try NiLiF (Nothing in Life is Free)...this means making her do something for you before she gets anything (including affection). I'll assume again that she knows how to sit...so make her sit before you give her anything (including food). Ask her once (don't repeat the word over and over again) and if she doesn't do it, don't give her what she wants. Leave it a while (5, 10 or 15mins) and then ask her again. If she doesn't do it, she doesn't get it at all.
For food this means that she doesn't get offered food again until her next meal (feed her twice a day and only leave the bowl down for about half an hour).
Basically this is just so she knows that you...all of you...control the household and the resources (ie: anything she wants/needs). Hopefully after a while she'll start to respect you a bit more.
Get your mum to correct her verbally (never physically) with a short, sharp "Ah-ah!" the second she starts to growl and when she stops she must be immediately praised for doing so. (actually this is something everyone in the house should be doing, but since she seems to respect your mum more I mentioned her)
She has to know exactly what she can do and what she can't and there can be no confusion. Once you decide on what's right and wrong, it stays like that.
Please...PLEASE bring that girl into your home. You'll enjoy her so much more as a pet and companion and she can be part of a family.
Now as far as the pup is concerned. I'm curious about how much socialisation your girl has had. Chihuahua's are actually known for dog aggression (they have quite a 'terrier' temperament) and must be socialised really well in order to accept other dogs (which they do easily once socialised).
If she's not been socialised it may be that which prevents her from accepting the new boy. She might feel a little threatened by him also.
Perhaps ignoring the pup while she's around and getting her to sit for you and when she's quiet and nice give her treats. Try to prove to her that the pup is a good thing.
Hopefully we'll have some trainers come online and give you more (and possibly better
) advice than me, but that's the way I'd handle it anyway.
This will all take time. Nothing is going to change instantly, you'll have to work at it and be dedicated. But that's all a part of dog ownership and personally it's one of the most enjoyable things about it...working with and teaching your dog new things.
Cass.