First off anyone that stop you in the street to ask you to breed your dog needs to be ignored! Breeding is not just putting 2 dogs together to make puppies. You need to know what you are doing. What is the purpose of this breeding other than to make a MIXED breed dog. This woman has a Yorkie/Maltese mix and want to mix it again with a Yorkie? What is the point and what is she trying to appomplish other than adding more dogs into this world.
My head is just spinning at this point the insanity of people and the lack of common sense that goes into their thought process.
You need to explain to your neighbor that his male could have a permanent change to his personality and not in a good way. I am not a breeder but I will see if I can find someone that can explain this better than I can. For the health of his male he should seriously consider having him neutered.