Highly recommend going to a 60 amp main breaker for the that sub panel. What size breaker are you using for the wire feed inside the main panel? What gauge of wire is being used for the feed to the sub panel?

There's no reason to change the main breaker in the subpanel or even to have a main breaker in the subpanel.

You should compute the actual load in the subpanel (which is different from adding the breakers amps in most cases) and use feeder conductors sized for that as a minimum. You then put a breaker in the main panel to protect that feeder (which is likely to be smaller than the 125A ampacity of the subpanel).