It's difficult to know how to respond.
On one hand, I want to see you succeed in getting any equipment you need to teach with.
On the other hand, your request for information is so broad-based and open, and your apparent understanding of what PLCs are and do so limited, that I'm not sure I can give a meaningful answer.
PLCs are everything, and nothing, to those areas you mentioned.
What PLCs do is CONTROL. They make things happen the way you want them to happen. Thus, they can be INTEGRATED into those areas, but they don't have to be.
Take mechanical engineering. A mechanical engineer can design a machine to work, with all the moving parts integrated mechanically to provide the proper feedback and control (think: internal combustion engine).
But a similarly functional machine could be designed (from a mechanical) standpoint to have a PLC control things instead (Think: Fly-by-wire in large modern airplanes - in the old days, turning the wheel controlled levers which moved the flaps. Later, turning the wheel caused hydraulic valves to open, controlling the flaps. Now turning the wheel sends an electrical signal to a computer (=~PLC) which controls the flaps).
Similarly, while a PLC is used to electrically control a modern factory, it is neither a necessity, nor a luxury. And there are many principles that an engineering student needs to understand first and foremost before being introduced to PLCs. Big concepts like: Control. Feedback. Usability (both from an operator and from a maintenance perspective).
And then there's the whole side of electical engineering (and not just electronics) that's never even heard of a PLC.
Same with textiles. PLCs can be used to make textiles. Or not. (and from what I've heard, most textile mills AREN'T PLC controlled).
I'm sorry I can't more for you. Perhaps others can give you better advice.