Yeah, this gets fun...

SSDT is the "upgraded" BIDS in 2012. In 2014, SSDT is now a completely separate download, either as a stand-alone (I hope as I just downloaded it at home) tool, or as a plug-in for VS.

I think to get VS to open SSIS packages, you'd need to get the SSDT plug-in for it. Here's the link I'm thinking of: https://msdn.microsoft.com/en-us/library/mt204009.aspx