I think I'd be happier if I could always default to my exosuit inventory, although I wouldn't mind an option to set a button for "most recent inventory" when I need to keep going back to the same non-exosuit inventory a few times in quick succession.
There is no way to open a specific inventory — only a single button that can bring up one of 4 inventories.
Which one? I think it's the last one you accessed, out of the currently available ones.
In theory, this could be convenient. In practice, this often makes the UI feel non-deterministic (also see https://github.com/lgarron/first-world/issues/175).
I think I'd be happier if I could always default to my exosuit inventory, although I wouldn't mind an option to set a button for "most recent inventory" when I need to keep going back to the same non-exosuit inventory a few times in quick succession.