Bellows design codes consider only angular rotatation movements for single hinged and gimbal units. Bellows designer will get totally confused if you give lateral and axial movements. He will come up with some very special and expensive design or tells you to get lost or declines to offer.

If you have two bellows units connected with hinge or hinges you give the designer lateral movement of the unit and specify double or single hinge arrangement, lengths, pipe material etc. If you specify axial movement you will get slotted hinges, if you specify rotation in addition to lateral the designer will assume that ends rotate.

I recommend you use EJMA form as a bases what you need to give to the bellows design company.

I am not sure that I can figure out your configuration. If you like send a sketch directly via e mail and I will have a look.