Boy is this a slippery slope question but I will give you my opinion having worked with rescue and our local pound. This is just my opinion and it is not meant to hurt any members who have large dogs with their Yorkies but to help you make a decision so no harm comes to your two little ones.
One of the things we always looked at from an adoption standpoint is, did the owners have other dogs at home and what size. While many members of YT have both big and small dogs from a rescue point we would not adopt out to someone with a big dog and I am going to tell you why. As many members know Yorkies are fearless and will attack another dog without a thought. Many a little Yorkie has died because of their Napoleon like attitude taking on a big dog. Even in homes where they were raised together this has happened, sad to say even to YT members. We just didn’t want to take the chance that the little dogs would attack and the big dog would respond and all it would take is one time and you would have a dead Yorkie. With rescue dogs you never know what you are really getting and especially what is in their history. Sad to say many a big dog once it got past its puppy stage was thrown out in the backyard and never taken care of. Many of these dogs have issues that you aren’t aware of until it is to late. It would also be sad if you brought in a big dog that in its excitement jumped up and then down on one of your little dogs back and broke it. Again, these things have happened and you have to decide if you are willing to risk your babies. Also looking over the list of some of the dogs you picked, i.e. the shiba inu, you are just courting a disaster based on the description from AKC. You really need to understand the verbiage they are using and what it really means. I am always so surprised at people thinking Yorkies are just lapdogs when in fact they are terriers and will kill a rabbit in 2 second. My pack has done it and it is incredible to watch them do what they were breed to do. It isn’t necessarily pretty to see them walking back to me with blood on their faces but boy are they proud of themselves. The other factor you need to understand is some of the bad breeding that has gone on and many of these in the pound/Humane/rescue groups came from mills or backyard breeders with absolutely no concern on what they produced. One place I would tell you to go is
www.petfinder.com and in the drop down box I would pick dog and then go look at each breed you are interested in. After awhile you might start seeing a history on some of the breeds and you start getting a clue what the breed is like. While many members at YT will tell you that Yorkies are great with children I would have you read how many of the rescue groups will not adopt out to families with children. Two reasons, the 1st is that many Yorkies just don’t like the noise and handling by kids and the second reason is kids without thinking step on these little ones and hurt/kill them. Many a child has been bit by a Yorkie and also turned into rescue. While I love the fact the two of you would consider a rescue I can not endorse a large dog but I can tell you if you find a dog on petfinder or through a rescue group some of the foster parents can tell you if the dog is good with other dogs but you will have to be on your guard. A good, breed specific rescue group wants what is best for all concerned and I know they would hate to adopt a dog to you that killed one of your little ones down the road. Please also remember your local pound or humane society might not be as concerned as the breed rescue as they are trying to save the life of the dog in the pound so be very careful.
I hope you understand along with the many YT members who responded here my stand has always been putting the dog first over humans and protecting these little ones as much as I can. Also, there are always exceptions to everything I wrote but you have to decision if you are willing to risk your babies.
Good Luck in your decision and please feel free to PM me if you have any other thoughts.