The only problem I see could be your hard coded parent ids (13,14,15,16). Are you sure those ids are set correctly? And do you really want to navigate through siblings of different parents at the same time? If not you could call your snippet with only the current parent like this:
[[!siblingNav? &id=`[[*parent]]`]]
[[+sn.first]][[+sn.prev]][[+sn.prevlinks]][[+sn.self]][[+sn.nextlinks]][[+sn.next]][[+sn.last]]
You could give "selfLink" a try. I never used this addon myself but sounds like it could be an alternative:
http://rtfm.modx.com/display/ADDON/selfLink