The answer to your question is yes. John and Joseph were brothers. Joseph was my great grandfather and the younger brother of John Thompson Muir.
All the Charlottes you find in this Muir family stem from the wife of of John Muir, Charlotte Thompson Muir, their mother and my great, great grandfather and grandmother. Charlotte died in a fire in 1848 and John remarried to a Elizabeth Croskery. She died in 1908 while John died in 1885.
I have alot of information on this Muir family and would be willing to share it with you.You can contact me directly at firstname.lastname@example.org.