I have Starbound on Steam and GoG, I like to co-op with my wife on a private server, after 1.3.2 she could no longer connect to the server using the GoG version, I went in and found it was still on 1.3.0, I downloaded the 1.3.2 installer, ran it, pointed it to the same directory but the game STILL says it's on 1.3.0 which keeps her from being able to connect to the 1.3.2 server. Any idea why it isn't updating properly? I'm downloading the manual installer, not using GoG Galaxy (haven't installed it on her machine)

Are you sure the new version isn't installing on a folder inside the old one?
Or did you take the wrong vrsion for her OS (64/32b)?

If the answere is no for both I have no clue about what is wrong. You can try unistall old version and install the new one. saves are inside "storage" folder, they should work with thee new version but better have a backup.