Anyone who is intentionally breeding such crosses is doing it for the financial reward and not the health/welfare of the animals involved. Breeding puppies is expensive and, if done correctly, costly, with little financial gain. This should make you question what corners these people are cutting in order to get their financial benefit from it.
Who ends up suffering? The dog and the new owners. I see it almost daily where someone had taken a poorly bred puppy on in good faith only to have to deal with a lifetime of health problems.
With this cross breed you'll be looking at things like:
Eye problems - chihuahuas have prominent eyes which makes them more susceptible to corneal ulcers, they also are known for lens luxation and glaucoma. Yorkie predispositions for eyes include KCS (dry eye), distichiasis, cataracts and PRA (progressive retinal atrophy - early blindness basically)
Skeletal problems - both breeds are predisposed to elbow luxation and patella luxation.
Both breeds are aldo predisposed to hydrocephalus, various heart problems and tracheal collapse.
There are tests that can be done to rule some of these conditions out (e.g. DNA testing for PRA), and other things, looking back through generations can help to see if there's anything being passed along the lines.
But only decent breeders will do these tests and a decent breeder wouldn't allow their health tested (very different to a health check from a vet) dogs produce cross breeds.
Obviously any dog comes with a risk healthwise, but steps can be made by breeders to reduce these. If your mum does go for such cross breed, or any dog in fact, make sure she takes out good insurance policy.