Let's see if I can guess whether you have the ability to train any dog, including the dogs you choose to breed.

Yes, I've had 3 generations.  I took them in when that backyard breeder got tired of them.

I have no problems.

Just like you, the backyard breeder I knew bred an AKC GSD with an AKC Lab AND boasted that both parents were full bred - why?  I have no idea.

I will not help a BYBer. BYBed purebreds are as low of quality as the pups they produced. BYBed bred to another BYBer, to another BYBer & it goes on & on. Quality going down, down, down.

I am ready to adopt another dog but I will not buy from a BYBer. I will adopt one that is up for adoption, even if it is the very same thing you are breeding.

ONLY if you spay/neuter all your dogs will they get along.  Otherwise you will have fights between the males and both are capable of getting your female pregnant again!

 Treading along that road will create great problems for both your dad   and the direct family members  and also the dogs involved.

That can , also lead to either serious injury or the death of the losing dog, and  serious injury to the victor very easily. As your dad obviously knows very little of the traits stamina and capabilities of such breeds.

Otherwise he would have removed the possibility of their mating occurring initially.

And would also know far better than to entertain such an idea as keeping any resulting pup to begin with.....

( I hope your dad  is rich enough to meet the oncoming vets bills....When the fights begin. )

This WILL NOT work out if either of the males remains INTACT and ideally Mom ought to be spayed, so they will have nothing to fight over - if she cannot come in heat.  None of the hormones will be instantly gone, even if all get fixed tomorrow.  So there will be lingering issues, for another month or so.

If your pup is 12 weeks, Mom could be coming back in heat RIGHT AWAY and this could get UGLY unless one or both males is removed, if you can't get her spayed BEFOREHAND.It is NEVER recommended to have two males, but esp if there is a intact female, also in house.  Working out pack order & who is "in charge" will be wildly up for grabs (and will become more of a problem over time) even if Mom gets spayed.  the younger son, may decide to fight one or both parents if he feels he should be the alpha, and it may be over time, as they have health issues or less energy.    Same gender dogs are not recommended in adoption or dog sales.  Opposite genders - always get along better. Males (if intact) are 75% more likely to bite people or to get into dog fights (due to testosterone).  So if you had to keep a puppy, a female would have been the better choice, IMO.  Many breeders ONLY keep female dogs and in most cases, they get along. It also does not work that way, in the wild.  One alpha male MAY keep a group of females but will DRIVE out..... all competitors, if they do not "choose" to leave.

IMO, this was not a suitable breeding to have let produce pups.  It does not help with over population of dogs and is NO improvement on either breed and was spawned by parents (who both have a number of health issues in each breed) and probably were NOT screened for any of them.  A GRAVID spay ought to have been done.  You ought to have ADOPTED another dog, if you felt you "needed" one.

Get them all spayed and neutered

Dog in the wild live in packs that are simply a family group. The whole "alpha" an "beta" thing is not true but a myth. They are all blood related and the males leave the pack when they are ready. The real problem is in domesticated dogs, when males can't separate from each other and are confined to a small area such as your house. 

Your males need to be castrated and your females spade to be honest. 

Totally unknown and depends on your skills as owners and the dogs temperaments although the same will apply if you keep a female and the mum might not get on with the pup when older.

As V says,  both being full bred doesn't help at all and I wonder if both were fully hip scored etc...I highly doubt it.   This mating should never have taken place that's for sure.

Instead of worrying about your pup,  how about worrying about all the others that you should have put contracts out with stating that they MUST come back to you should they ever need rehoming in their 10 / 12 yrs of life. 

This is a total unknown.   They may get along well, depending on whether you do the right thing and have mum spayed - for sure they won't if she's allowed to come into season.

Both being purebred of their breeds doesn't help - in fact I wonder why on earth you allowed this mating to happen in the first place.