Which parent should start the process?

As you start the new sleep plan, consider.....

- which parent will implement the plan best and be most consistent
- which parent the child will respond best to

That is the parent who should start off handling the new sleep plan and get the child used to it.

If the child really wants one parent over the other, that may not be the best way to make the decision.
Remember, we are moving towards sleep independence so if the child is used to falling asleep on mom or seems overly attached to mom, although she may want mom, she may actually protest less for Dad. Thus, making Dad the right choice to start the process. This is a decision that you have to make within your family.

I firmly believe parents should be able to alternate bedtime responsibility if you want to.
So, once your child is more used to the new routine, give the other parent a shot.
Just make sure the other parent handles things the same way and has a good understanding of the rules.