New female chihuahua marking in the house - crate trainning?

I just got a 2 year old female chihuahua today. She's a very sweet
dog, and very well mannered. She's perfect, except for the fact that
she wants to pee in 4 or 5 spots in the house. We have another dog,
so I think she may be spotting, even though I've never heard of a
female dog marking its territory before. Is this common?

Is she trying to tell me she wants to go outside and use the bathroom?

Will crate training keep her from doing this?

Any help would be appreciated. Thx