The rating and type of the MCB's will, if the system has been properly designed , be correct to protect the cable (at the head end) and separately the installation at the hut end, with discrimination such that a 'local' fault stays just that.. To have MCB's identically sized is not ideal and may be totally incorrect, indicating that the installation was possibly just guesswork.
If you are only using one bit of machinery at a time the 32A MCB in the hut could be sensibly replaced by one rated at 16A but that won't necessarily stop the tripping problem.
A physical check of all connections (phase neutral and earth) from end to end plus checking earth integrity on the equipment is a good idea.
MCB's can be supplied or even go trip happy so a direct 1:1 replacement of all the existing protective devices might possibly 'fix' the problem.
Simply swapping the an MCB from a type B to a type C or even a type D without being fully aware of the implications of such a change is not a sensible idea. It might not provide enough discrimination which is what you are after and it could degrade the effective level of protection on the cable from the head end to the hut end.
But as ever, without having sight of the installation, the earthing arrangements and measurements of the fault level most of this advice is just 'guessing'