In the Biblical New Testament, Calvary is the hill where Jesus was crucified. In modern usage, the word’s other definitions are (1) an artistic representation of Christ’s crucifixion, and (2) an ordeal involving great suffering. Cavalry is completely different. It refers to (1) the part of an army that fights on horseback, and (2) a highly mobile modern army unit. Because the only thing separating these two nouns is the placement of the l, they are easily confused.
Calvary is a proper noun (thus capitalized) when it denotes the hill or a work of art. When it denotes a difficult ordeal, it is a common noun and does not need to be capitalized. Ignore what your spell check says.
The use of calvary in place of cavalry is common—for example:
Wiseman was gone from the homestead after joining the Nebraska Calvary of the U.S. Army to fight Indians in Dakota Territory. [Yankton Daily Press]
Dr. Rival discovers an aortic tear and calls in the calvary. [TV.com]
The reverse error is rare, mainly because the word calvary is rare.
These writers spell the words correctly:
Nieve couldn’t imagine the calvary he was about to go through. [Cycling News]
The last time the British Army used horses in a cavalry charge was in the Second World War. [The Sun]
Within the pillar is a treasury in which is kept what is claimed to be the cloth with which a woman named Veronica wiped the face of Jesus on His way to Calvary. [The Record]
If you want to see the military do what it does best, then ride out on a mission with an armored cavalry squadron. [National Review Online]