Hoping to hear from any dog behaviour experts (or just anyone with experience of this!) Asking on behalf of DM, who is at the end of her tether and frequently phoning up to rant! Parents are in their 70s. They've recently brought home a new puppy - she's a 13 week old Coton de tulear, who was meant as a companion for their 6-year-old Bolognese (both bichon types - I realise they're not exactly the best known breeds!)
Basically it's been a bit of a nightmare from the outset. Their older dog (also female) hasn't been socialised particularly well - she's a typically pampered lap-dog, who hasn't been allowed to 'be a proper dog', barely goes off the lead (unless she's out with me and DP, as we sometimes dog-sit) and is often timid with other dogs on walks. She hates the new puppy, who is quite bouncy and full-on - puppy is jumping on her back, nipping ears etc and older dog is reacting either by snarling and baring her teeth or by freezing, cowering and looking terrified. The puppy, meanwhile, is obsessed with her and won't leave her alone - three weeks in, she doesn't seem to be picking up on the older dog's 'leave me alone' signals at all. This seems odd, as this aside she's proving to be a very quick learner in terms of general training and manners. The older dog has become more clingy and whiny since the puppy's arrival (she was pretty bad with separation anxiety to start with) and DM now suspects she may have recently begun wetting around the house, where previously she was perfectly house-trained. According to DM she's basically 'lost her sparkle'.
My parents really aren't coping, and are now on the brink of rehoming the puppy. They've sought advice from the vet, puppy's breeder, various puppy training guides and local puppy training classes and the consensus is to 'give it time', but there doesn't seem to have been any improvement so far. Tbh I'm quite cross with DM about the whole thing, as I suspected this might happen and strongly advised against getting a second dog, but she's very bloody-minded and went ahead anyway. She's also quite impatient, and seems unwilling to wait it out until things potentially improve. 
Is there any light at the end of the tunnel with this? Will some dogs never accept a younger puppy? DP and I live nearby, and have tried to help out as much as we can, but it's incredibly stressful seeing my parents so stressed out and both dogs so unsettled.