I have three Yorkshire Terrier girls now, various ages and we want to get a male Yorkshire Terrier pup and a Goldendoodle male pup. Will they fight for dominance down the line? I am worried about the male Yorkshire Terrier.
It doesn't matter if you introduce a male or female dog do the family, the hierarchy will always be disturbed and reestablished.
Some dogs are more aggressive, others timid while reestablishing the hierarchy. That's mostly influenced by their individual characters, but male dogs tend to be more dominant. That doesn't mean there are going to be physical fights among your dogs. On the other hand, if 2 dominant females are introduced to each other, they can fight just as fiercely as males.
In general, pups will behave submissive until they reach sexual maturity. If you don't want to breed them, that's also the time to desex / neuter your male, which has the tendency to make him less dominant.
To avoid physical fights among your dogs, you should be the most dominant pack member and keep the atmosphere friendly between all dogs. If your current dogs are obedient and follow your command, and you feel confident to train and care for the new pups just as well, go for it. If your dogs often do things you don't actually want but you feel like you cannot control them, adding more dogs will only make the problem worse. In that case I would advise you to reconsider.
While ultimately it is going to come down to their personalities, getting two puppies of the same sex at the same time and having both of them hitting maturity around the same time is going to make it way more likely for you to have issues. This does not come down to needing to be a strong pack leader or that you need to be dominant over the dogs.
Sibling Syndrome (also called Littermate Syndrome, but it happens to dogs who aren't littermates as well) is the term for common behavioral problems that arise when two puppies are raised together beyond the typical 10-12 weeks (about 3 months of age) that professional breeders recommend. These common problems stem from improper socialization during a puppy's crucial first 6 months, and are why any responsible shelter/rescue/breeder would deny letting someone get two puppies of similar ages at the same time. It is almost impossible to raise two puppies without them going to one extreme to the other - being so attached to each other they completely shut down or panic without the other, or them hitting maturity and trying to seriously hurt or kill each other.
Given the potential for the size difference, you are right to be worried about the smaller dog in this instance. If I were you, I would look at which dog would be a better fit for your home and lifestyle rather than taking home both puppies. If the two puppies end up coming home with you anyways, I would get in touch with a certified behaviorist right away to prevent any issues from arising.
Here are a few sources to read up on SS/LS:
There is a common misconception that wild wolves, and by extension dogs, form packs in which there is a dominant "alpha male." This idea was based on incorrect research. The research was carried out on wolves that were kept in captivity in conditions that for humans would be considered those of a prison. Wolves in this unnatural situation do not behave as they would in the wild. In the wild, packs are normally family units, and there is dominance only in the same sense that the parents in a human family tend to dominate their children.
Dogs have some behavioral and biological differences from wolves, but the notion of an alpha male and a strict dominance hierarchy is no more correct for them than for wolves. Most of the world's dogs are not house pets but rather they have a lifestyle in which they form more casual alliances and contacts with humans, who give them food. Examples are village dogs in Africa or dogs that live in garbage dumps in Mexico City. These dogs guard resources from each other to some extent, but they do not form dominance hierarchies.
So if you bring new dogs into your household, there is no particular reason to expect that they will fight for dominance because of some behavioral programming encoded in their DNA. Conflict is possible, but can be dealt with by common-sense measures such as making sure that each dog's food dish is far away from the others'.
Mech, L. David. 1999. Alpha status, dominance, and division of labor in wolf packs. Canadian Journal of Zoology 77:1196-1203. Jamestown, ND: Northern Prairie Wildlife Research Center, https://digitalcommons.unl.edu/usgsnpwrc/381/