I favor the use of "chemical-mechanical" (with an en dash, not a hyphen) for the following reasons:
Quite a number of such Russian plants describe themselves in this way, in English, with said English formulation specified in official documents. (That said, I am aware that some number describe themselves as "chemical and mechanical" plants, too.) Whatever a business may call itself (short of something completely pathological), I am of the opinion that whatever it calls itself is what it should be called, and thus, whatever such plants typically call themselves is an acceptable (and I would go so far as to say preferable) translation.
If "process equipment plant" tickles your fancy, then in this context it must, in my opinion, have "chemical" tacked onto the beginning, because a plant that manufactures machines to process, say, breakfast cereal is equally a "process equipment plant." (In fact, I think you'd be better off with "chemical equipment plant" if you want to avoid the chemical/mechanical naming.)