I am considering adding another yorkie to my familiar....preferably a lil girl

After learing about puppy mills and realizing I got Pepe from BY Breeder I decided to go through a rescue rather then a breeder. My question were.....do you know about how long the whole application process takes and I have heard that Rescues do not allow someone to adopt when they have young children? This concerns me as I have 2.5 year old girl, but she is wonderful with Pepe....I took a great amount time to teach her how to be gentle with him and would never leave her alone with him (just in case). I saw a precious girl on their site and was just wondering if anyone could help me find out this info.
Thanks,