My dad's my friend on FB, his other friends are my three best friends, one of my sisters, my cousin and 2 people I don't know. He likes looking at the photos, sometimes he even writes on my status.... I've no real issue with it. I quite like that he's there in the background really. :c)
You say you saw the names on the Ipad thingy, is that the family ipad or is it just your mums. If it's the former then she's clearly not hiding what she's doing, maybe she wants you to ask her about it. If it's the latter, then it's probably just as bad you snooping on that as her snooping you. (I'm actually assuming it's the former).