MyJorDash,
I was thinking about something you might could do this time around if you don't mind my imput here. Of course I'm not aware of your financial picture and realize that you have quite a lot already invested between the 2 dogs and the driving back and forth so many times.
If your finances could afford it, as well as if you are working you could get a day off, maybe you could plan to make your pick up for the replacement pup on a Friday. Perhaps your mom who lives next door would be willing to give you a weekend off and keep the kids for you and you or you and DH could make a little weekend out of it 2 hours away where the pup and the breeders vet are located. If this is possible, you could arrange to pick up the new furbaby on Friday afternoon, early? and check into a motel in that town and just put your feet up and eat out and spend some quiet time not only to relax your nerves, but give yourself some observation time without the back and forth long distance travel in case something goes wrong. Bring a crate and woowbie for the crate as well as a small feeding dish like what is used for cats. The small very shallow one which could be placed in the crate with the new pup. I would suggest a supply list such as, heating pad to be placed under the crate on the underside set to med, then a blankie to seperate the baby from the pad a little more. I would also bring some nutracal, baby food (my choice, plain old rice ceral mixed with puppy milk) as an initial diet. It is so bland that it shouldn't irritate the puppys bowels regardless of what might or might not be brewing on his insides. I would take the baby to the breeders vet the next day (Saturday) and get his thoughts in writing asking him to write ledgibly so that you can read his comments, temp, diagnosis, concerns, treatments etc. Again, finances permitting, Stay over again Sunday, just relax cuddle with the pup some in a room which will obviously quiet and semi dark and just observe with a notebook times, events, puppy behavior, feeding success or failure etc.
On monday morning if everything is looking good I would get up early if you work and make the trip home so that you only missed Friday. Keep him crated and ask your mom if possible to keep up with your observations in your little notebook on Monday and then Monday evening or whatever your work schedule is bring the new furbaby to your own vet with the copies of the vetting done by the breeders vet in hand.
By now you should have been able to rule out the first pups affliction given the time frame involved. The pup would have made the transition in the least possible chaos or commotion, and the children could be introduced to the new baby all the while keeping him in the crate and avoiding any extra handling. This will not only build up your confidence that what happened last time won't happen again, dispelling any fears that you might be harboring in regard to self blame. It will also protect your children to exposure in the event it happens again, but spare them the sadness of losing yet another little furbaby.
Also, if on Monday am you find that something is wrong with this baby as well. I would go directly back to the breeder with the pup, with whom nobody has done any lasting bonding with up to this point and ask for a refund.
OHHHH I forgot to mention the most important part of this weekend trip. Pack some candles, some great bath oil, a snuggly robe and a good book on everything you wanted to know about yorkies but were afraid to ask and settle into a much needed recoup that at this point you well deserve.