Your Father is fortunate to have someone so interested in his well-being and that of his caregiver - your Mom.
Hallucinations can be caused by meds. I would definitely talk with his neurologist about the hallucinations. Another resource on meds would be the pharmacist. Hallucinations are not good and can often be addressed by a change in dosage or change in medication. As previously mentioned, hopefully your Father is seeing a movement disorder specialist (MDS) which is a neurolgist who specializes in movement disorders such as Parkinson's.
You also mention that his caregiver, your Mother, is exhausted. That is a concern in itself. Caregivers are angels. Those of us with PD are forever indebted to our caregivers. However, a caregiver needs to maintain their health as well. This is a challenging balance act. Hopefully your Mother can find someone to assume that caregiver role for a few hours each week - she needs that time. The temporary relief could come from a family member, friend or adult day care. A caregiver support group can also be very beneficial. Caregivers often feel guilty taking time for themselves ... but maintaining their health is as important as assisting the person with PD.
Best of luck!
Life is a dance. Don't sit it out. ---- Jackson H. Brown