I would advise against this at this stage. You need to clarify your case, including those elusive objectives, and then determine the information/evidence that you need, and you need to do this with help from a union official.
Tying management up with subject access requests (they will spend all their time looking at ways to minimise what they need to show you, and making sure that what they give you is unhelpful) is not necessarily going to further your claim, if you decide to make one, and can be distracting and unhelpful.
On the other hand, if the union people think it is helpful, they will, hopefully, take proper advice about the exact questions to ask, and the exact information to seek, and the words to ensure that management are not able to avoid providing this. If you have already submitted a subject access request which covers similar ground, management will ignore the one from the union if they possibly can.