Hi Bernadette and welcome to the Forum
You are absolutely right that online selling sites are the worst place to look for a puppy and are used primarily by puppy farmers and poor quality breeders. There is a link here to two breeders who are registered on the Kennel Club Assured Breeder Scheme in Northern Ireland and, if they are breeding to the ABS standards, should be a good place to start looking for a well bred puppy. They are subject to inspections by Kennel Club regional assessors and must abide by the eye testing schemes for miniature schnauzers.
https://www.thekennelclub.org.uk/servic ... 96&area=11
The best way to find a well bred puppy is to seek out a breeder first, check them out yourself fully and then see when they are going to have a litter of puppies next. It really is risking getting a poorly bred puppy if you look for puppies advertised online and set a specific time or date for getting one.
I do understand your wish that your family get a puppy at Christmas time but it is highly unlikely that a reputable breeder will let a puppy go at the festive season. It is partly, as you say due to people casually buying a puppy only to discard it after Christmas but also very much because Christmas and New Year are generally not a good time for a young puppy to be going to a new family. The noise and excitement, visitors, different routines to normal everyday life can be intimidating for a young animal and the need to be house training and establishing normal everyday activities with the puppy will be almost impossible to put in place at Christmas for a family with children.
If you can find a good breeder (the ones listed on the link I gave above may also be able to recommend good breeders who are not on the ABS) then discuss with them a future litter and maybe a date not too far after Christmas. As your family already know the puppy is not coming from Santa, if you do find a good breeder who will have a puppy for you early next year, you could ask the breeder if they would let you have e.g. a photo of Mum (maybe Dad) of the pups to come or be able to let you meet the Mum beforehand etc. That way the family can enjoy the forward planning of the litter, or (if there are pups which could go in January) arrange visits at some time suitable over the festive season.
We waited until January for our very first miniature schnauzer puppy and did not regret it. House training can be harder in the cold wintry months but, if you are set on a puppy in the coming months, do look for a good breeder and work round getting him or her after the excitement of Christmas as it will be better in the long run I am sure.
If anyone can recommend a good breeder in Northern Ireland for you, it will have to be by private message and do always check them out yourself before you commit to taking a puppy, not only to avoid puppy farmers but so that you find someone you feel comfortable with and trust to advise, support you, if needed with your puppy throughout its life.