Sounds like they each need to be independent.
See https://youtu.be/nlcLp47lGiY?t=8m17s - it's an older example (stapling has been removed in the latest release) but it shows the difference between independent or not.
If they are and this is still happening, can you please File > Export > Puppet and share it as a link (Creative Cloud, Google Drive, Dropbox, etc.) so we could take a closer look?
Yeah, the wings are both independent. I've exported the puppet to Dropbox. How do I PM you the link? Thanks!