As far as I'm aware, it should be heard by an outside manager. Though, this won't guarantee them being impartial.
Your Rep should be there. You may ask about an Area Rep being there instead, as they may be more knowledgeable about procedure, though I'd expect your Rep has sought their advice already.
They are pressurising you to keep it in house for one or two reasons. Maybe both.
If it stays with them, they can ignore it/hush it up/take zero action. Then you lose, before it's heard.
They may be willing to deal with the issue now, but want to keep it quiet so they don't get asked questions by others about their actions/failure to deal with it sooner.
As for being held on a different shift pattern, it is acceptable.
But' I'd insist on it being during my duty time, it's a work related issue, and it's probable they don't want to have to cover/pay for your duty to be done by someone else.
My own Rep, when dealing with these types of things, always asks for them to be dealt with by a manager OUTSIDE of our Area, as most managers working within the same 3 or 4 postcode areas will know each other, and may very well be mates. Even if they aren't, there may well be a nod and a wink situation going on.
You want it to be dealt with by someone who doesn't know you OR the person your complaint is against (especially if that person is a manager).
Good luck.
