I cannot imagine someone rehoming a 5 year old dog because she did not get along with one of her puppies they kept!!! You rehome the puppy if necessary, not the 5 yr old! It is MUCH harder on the 5 year old to upset its whole world like that. It might be because she was NOT really house-trained, which is a sad reason.
It is natural to have a rough few nights at the beginning of any new pet. Their whole world has just been turned upside down, no matter how nice the new world might be. It takes a lot of patience that first week or two. You may have to take her out quite often, until she gets the idea thta she goes only when you take her. Every 2 hours is about right for a new puppy and you may have to treat her as a new puppy. Hopefully, you will be able to develop a rhythm with each other. Her spreding out her times, and you noticing when she actually does something outside.
I do hope your yorkie is on the large side. It is really not the best choice for toddler age children. They tend to not understand fragile bones and delicate trachea. You will have to watch them constantly. I would set some rules immediately -- no carrying the dog, no picking her up, no holding her at all unless you are sitting beside them. It takes so little to hurt these precious toy breeds! Hopefully your children will be extra careful. Some of that age are more mature and can handled the rules needed with one so small. You may want to look at the "stickies" at the beginning of each folder. Some of them are especially informative for new owners. You may want to go back to square one as far as house-training since it is a new environment, and a new method (no doggy door) as well as she may not be that well trained anyway.
As far as food -- Royal Canin is available at most pet stores in the states too. It is a medium high quality food. I like it for the most part. My dogs really like it too. When I run out of their normal mail-order food, I feed Royal Canin and I mix with whatever I have left of the other brand. They pick the Royal Canin and leave the rest every time.
I am not that crazy about IAMS but it is not a bad food. We get real picky on YT sometimes when it comes to food, but I think there are plenty of dogs that are doing well on most brands. Still, if you want the beautiful coats, the nice tiny tootsie-roll poops, the healthiest skin and bones.....might want to go up a step or two in quality.