Can the body corporate use an exclusive use car park for trades' parking and storage?

It’s impossible to respond definitively, given that each situation and exclusive use by-law is different. That said, your general rule of thumb is that an exclusive-use area (be it a car park or something else) is allocated for the use and enjoyment of the party (occupier or owner) to whom it is allocated. In other words, if you have an exclusive use area, it’s generally yours to use, subject to the terms of the by-law, and it doesn’t become a general use common space.

There is a legislated process for amending an exclusive use by-law, and that process does not involve a unilateral committee decision. While a body corporate does have a legislative right to enter a lot, as you point out, that right is limited to specific purposes and requires notice. This situation doesn’t appear to be about the power of entry, though.

It may be the case that your exclusive use park is convenient. Or that parking is scarce, and yours is the only spot available. Even if either of these is true, that doesn’t empower the committee to use the space as they see fit and when it suits them. To be blunt, ensuring contractors have a car park and space to store tools isn’t your problem or your responsibility.

This is general information only and not legal advice.