In general, there are 3 different types of ataxia. Since you are not seeing head tremors, intention tremors, or a truncal sway, it is less likely that a vestibular or cerebellar ataxia is the cause of Squeaki's problem.
This means that it is probably a sensory or proprioceptive ataxia. In this condition, the spinal cord is being compressed and the nerve signals sent from the spinal cord are not reaching the limbs as they should. The result of the placing exercise that your vet performed is consistent with this type of ataxia. Proprioceptive deficits (inability to know where the limbs are in space due to disruption of nerve signals from the peripheral nerves in the limbs to the spinal cord) are one of the earliest signs we see with progressive compression of the spinal cord. Weakness of the limbs may also be seen.
Since all 4 legs are affected, the problem is most likely involving the cervical vertebrae (the ones higher up in her neck, before the start of the rib cage).
Possible causes of Squeaki's problem include:
1. Hemivertebrae- these are abnormally shaped vertebral bodies that can result in kyphosis (dorsal deviation of the spinal column) or lordosis (ventral deviation of the spinal column). These can often be detected with careful palpation of the spinal column. The abnormal deviation can cause compression of the spinal cord, thereby impeding nerve signals. Hemivertebrae are most common in chondrodysplastic breeds (smoosh- faced, twisty legged dogs such as your Shih-Tzu). These dogs can start off normally, then as they are developing/growing the hemivertebrae causes a progressive compression of the cord and subsequent neurologic signs.
2. Intervertebral disk disease- a disk between the vertebrae butts up into the spinal column and causes inflammation of the spinal cord. This is a condition more commonly seen in dogs with elongated backs; chondrodystrophic breeds like Shih Tzus are also pre-disposed.
3. Atlanto-axial subluxation- absence or underdevelopment of the dens, a structure on the 2nd cervical vertebra, causes instability between the 1st and 2nd cervical vertebrae resulting in spinal cord compression. More common in small breed dogs.
4. Infectious problems such as discospondylitis or myelitis. These animals are typically sick, however. Fever, lethargy, decreased appetite, and significant pain are common signs. If Squeaki is not experiencing this, it would be less likely in her case.
5. Tumors- pretty rare overall, and very rare in young dogs.
As to your question, B vitamins won't hurt, but unfortunately I don't think they are going to help in this case.
Your very best bet is to be referred to a veterinary radiologist who can perform a myelogram. This involves injecting dye into the spinal column to outline the area of compression of the spinal cord. Surgical correction of the problem is the best fix.
Plain radiographs, that can be done at your local vet, would help to rule out abnormally shaped vertebrae, lordosis or kyphosis.
I hope this information was helpful and that you are able to find help for Squeaki.