I recently bought a 2 month old shitzu/maltese I've had her for a month, but I've noticed something odd.
Whenever my dad goes to pet her or pick her up, she pees a little inside the house. she walks away really sudden and as he approaches her she still pees.
And as he picks her up she lays down and puts one leg up. Is she scared?
Hi Waslat Your puppy is adorable, what a cutie!
What you're describing is submissive behavior. She senses that your dad is the head of the household (or in dog language the 'alpha') and is trying to show him that she understands that and is not challenging his authority.
The weeing is called submissive urination and is fairly common. The best way to handle it is to totally ignore it, if you draw attention to it or get mad at her, it will make her pee more! That's because she will misunderstand you and think that she's not been submissive enough and try even harder.
Keep homecomings etc. low key and ask your dad to ignore her for 5 mins or so after he comes in, then approach her quietly and just pet her a little, using a low voice. If he avoids eye contact and crouches down at her level when petting her that will help as he will seem less threatening to her.
She will most likely outgrow this behavior as she becomes older and more self confident.
Lying down or rolling over and showing her belly are also signs of submissive behavior. Again, she's showing that she recognizes his position as being far higher than hers.
You have a beautiful pup who sounds as though she's very sweet natured. Best of luck with her!