Okay, I guess I got my questions mixed up. You’ve asked a couple of related questions dealing with Dataset. In this one, Plot specific named columns of a dataset , I showed you how to extract two columns. In this one that we’re now working on, I’ve already showed you how to turn dataset columns into a list of pairs that can be fed to Interpolation. If you just put it all together, you can get what you want.
(* From this current thread... *)
Normal[Values[dataset]]
(* ...gives you a list of pairs*)
(* From that other thread... *)
dataset[All, {"t", "v"}]
(* ... extracts columns from a Dataset *)
(* So, just put it all together *)
Interpolation[Normal[Values[dataset[All, {"t", "v"}]]]]