Need advice re new rescue dog & resident dog

We have a 10yr old extremely sweet natured dog friendly spayed female who is westie size & well mannered with all dogs & happily welcomes any dog into our home respectfully reading all signals & behaving accordingly. We frequently have friends dogs to stay for holidays & even strange dogs in emergency’s etc. & our dog happily shares with all... big or small..old or pups..quiet or boisterous.
We have taken in a tiny 5yr old female yorkie (natural) who is learning to walk after a spinal operation, she can walk but is wobbly on her back legs & the idea is being with another dog will encourage her progress to build strength in hind legs. We have only had her a week & she has settled well, she is confident, knows her way around, eats well, let’s us know what she wants, she plays with toys on her own with our dog present, wags her tail a lot, is very loving & has settled into a routine. Although they don't play or interact together the two dogs eat together & co exist no problem, they are fine on walks both on & off lead. They are both fine meeting other dogs on walks of either sex.
The problem is the little one often lunges & snaps at the older dog in the house for no apparent reason, she curls her lip & stalks her. The older dog doesn’t interfere with her at all, is happy to be sniffed & gives her space respecting the little one doesn't want to interact & cowers whenever the little one goes for her & never retaliates. Now the older dog is afraid to go near her & passes her with a wide birth just in case. She doesn’t come to us when called if it means passing the little dog & is beginning to look depressed. I am fearful this very sweet little dog is going to break our dogs gentle spirit if it continues. We want to help this little dog & being with our dog is making her use her legs much more than she was but our own dogs well-being is important.
Any advise would be appreciated please.

I would take notice of your resident dog and if this continues i would be looking to rehome the yorkie ...not all dogs get along happily unfortunately. ..it may get better in time but you may have to face that it might not ....

The other thing I would possibly think about is if the yorkie is now doing more maybe she is feeling a bit sore and warning your dog to keep away maybe? It is always tough taking in a new dog especially one that is in recovery but I would also have to echo what Tinytom says above for the sake of your lovely natured dog, albeit a hard decision...

Thank you for your responses. It is tough as the little one is very sweet in all respects and has had a long recovery journey. She is a tiny 3kg and must feel vulnerable despite being loving bold and determined bless her. Every thing here is perfect for her and she is doing so well. I don’t treat her like a delicate flower and let her know the snapping and stalking is not acceptable by moving her away and ignoring her, not do I pamper my older dog i just reassure her. I am proud of them both, even if not close buddies I just wish they could live in harmony. I will persevere for bit longer but know we may have to make hard decision about keeping the little one

There will be other equally good homes, so don't beat yourself up about it. We don't like everyone we meet either, never mind living with them.

I was in the same situation with an older dog and a newer smaller one, both rescues, it started with stalking then she became openly aggressive towards the older dog and they had to be separated, some dogs just aren't meant to be together!