Impurity of a dog

Q: Two days ago, there was dog sniffing the pathway for a long time. I saw a small handful puddle of wetness. So on that area I pushed the pram back and front again twice. After couple of days, my son used to play with the pram tyre by rolling it on his hand. He did that with wet hands and touched utensils with wet hands to eat and below where I have later placed utensils on top when wet. Now I know if a dog licked it we have to wash the earth 7 times. Now because of the saliva that has spread on my house must I wash each utensil that have been touched by him. 

Wali of a girl whose father does not want to be present for the nikaah

Q: I was divorced 20 years back and I have 2 daughters from my first marriage. My parents brought them up without any help from my ex husband.

After divorce, he got married and I also got married. Now my first daughter is getting married. For some time my ex husband is contact with my daughters so she asked her father to be her wali in her marriage but he refused all of sudden.

My father, their maternal grandfather (nana) became her wali from the age of 2 since he only taking care of her.

My question is whether my daughter's marriage is valid or not?