Honestly, if I were a Mom, I would not be searching for my young toddler to have a Yorkie (or small dog for that matter). If you have friends and family with them, that's great, have some play dates, but to want to get a Yorkie for a young toddler is probably not the route I would go. Also, being that you don't want to spend a lot of money, that may be a problem in the future, as most Yorkies at some point require expensive vet care, or 'if' an accident occurred with the young toddler and yorkie (hey Britney Spears' Yorkie broke it's leg by her kids playing with it), would you be prepared for that
This isn't the route I would go if I had a young baby/toddler/child at home to care for