I think mother's pins are really special. I hope to get one someday! My thoughts on your questions:
If your daughter joined your sorority and gave you a mother's pin, how often would you wear it? Alone or with your badge?
I would wear it alone AND with my badge in any situation calling for badge attire...I don't think the mother's pin has the same rules that the badge does, so I'd probably get to wear it more often.
If your daughter joined a different sorority from yours and gave you a mother's pin, how often would you wear it? Alone or with your badge?
I'd have to check and see if our rules conflict, but I think I would wear it to functions sponsored by her sorority, but with my golden lamp badge, placed just below (if the situation required badge attire). I know we can wear fraternity badges of our husbands or Order of Omega pins, but they have to be below the DZ badge. If it was not badge attire, I'd wear the mother's pin, but then wear my DZ crest necklace to show my affiliation. I think to receive a mother's pin would be incredibly sweet, and I don't really think it would signify my being loyal to her sorority, but supportive of her membership in that sorority....
If your son joined a fraternity and gave you a mother's pin, how often would you wear it? Alone or with your badge?
Same as above, but I'd probably wear it to my own sorority functions as well...
If you had several kids who went Greek, how would you handle your collection of mother's pins?
I only have 2 kids, so it would probably be manageable...but more than that, I'd probably just wear them one at a time.
For those of you whose orgs offer mother's/father's pins, what rules do you have regarding where and when they're worn? (e.g. must be in pin attire, not to be worn while consuming alcohol, etc...)
I'm not sure there are any written rules regarding our mother's/father's pins...maybe some other GC DZ will know? I've never given one b/c my Dad wouldn't wear it (he's in construction!) and my mom passed away before I got to college....