Cheri,
Did you ever find out any more info on this group? I am guessing it was NOT the official one where a member is approved by the Pope and must be catholic. My ggm was vehemently anti-catholic yet her 1955 obit, from far eastern PA, says "she was a past president of the Jean de Acre Sisterhood, Dames of Malta." I have two pins that my mom claims were from DoM. It LOOKS like the Pope's Knights and Dames of Malta except the colors are reversed so it's a RED cross on a WHITE background. The red also appears to be a few shades darker than on the other one which appears to be a BRIGHT red.
Anyway, I am wondering if anyone knows of these groups! My mom says her mom attended a National Convention in 1939 in NIagara Falls with her mom, but it may have been for yet another unknown lost group called Companions of Friends. My mom does think DoM must have been a secret organization because she had to sit in the room outside while her mom and g mom attended the actual meeting. Your group sounds like it may have been the same sort of thing and fits the same time frame about 1910 to 1940/55. Anyway, just wondering.....