This is how, as far as I understand its meant to go as a basic format:
First reading- Bill read out in one of the Houses to allow MPS/peers to prepare and debate at the second reading
Second Reading- Debate and discussion
Committee stage- In depth discussion of the minutiae of the Bill by a committee of MP's
Report Stage- Amendments by the Committees discussed
Third reading- The final draft is read out and voted on. It is then passed to the other House to go through the same stages.
Royal Assent- Rubber stamping by the Monarch- This cannot be refused by convention and is what would cause a Constitutional crisis if they did so.
What it looks like happens before the first reading, and at drafting stage is that the Monarch and the heir can just decide they don't want the law to apply to them. (@Puzzledandpissedoff am I right in saying you are saying exemptions should only happen on the advice of the government, but in practice, the government just rolls over?)
This is then written into the bill before the first reading (see above) By the time it gets to the third reading, of course it cant be changed, because nothing can. It is also not discussed at the second reading or presumably Committee stage because Parliament have decided that they don't discuss Royal matters. So we have a situation where King says 'Jump' Prime Minister says 'How high?' then it just gets drafted into the bill and goes through all the stages. The King then has 'no choice but to consent' to something they requested in the first place. I always thought those 'red boxes were just useless busywork, but turns out they are intended to make sure the Monarch isn't caught out having to do something they don't want to do, like adhere to environmental protection legislation.