Can I be sponsored under the AINP family stream if I already have a Skilled Worker Class application for permanent residence in process?
Yes. The decision to apply to both programs is up to you. However, depending on the processing status of the Skilled Worker Class application for permanent residence, there may or may not be an advantage to applying to both programs.
Source:
http://www.albertacanada.com/immigration/immigrate/familystreamfaqs.html#37PS: Keep in mind what Bety has informed as She has personal experience on the matter.
Good luck