Congratulations. We adopted Snowball last December and it took about a month for him to get use to our other dog Toby. I was worried at the time but just kept an eye on Snowball and now he's Toby's ears as he is deaf, bless.
I totally agree with rescuing a dog and like you, Snowballs first mummy went into a nursing home. He was on meds for anxiety and needed a lot of dental work. One year on he's a happy, healthy, loving velcro dog.
Enjoy them both, pets bring such joy to our lives.