Congratulations on the new Yorkie Poo! I'm sure with a little TLC and a little bit of training, those negative issues she is experiencing will go away. Moving to a new home after three years is a big transition. I'm sure in no time she will be fitting right in.
I groom my own dogs, but I must say ... I'm just as likely to "mess up", and give my dogs a cut I don't like, just as much as any groomer. However, it is easier on both of my dogs for me to do it myself. I'm sure after a nail trimming and grooming session she will be so comfortable!
Sometimes (not all the time) if people cannot provide documents of vaccination for the pets they are selling, it is very unlikely that the dog actually ever did receive them. So, hopefully you're able to find all her vaccination records. If you can determine what clinic that dog was taken to, I'm sure they can help you locate her records.
Congrats and the new member of your family

! Hoping she settles in perfectly. We would love to see pictures of her if you have any