Upvote:4
As a matter of law, a UK national is not supposed to get a UK visa. A dual citizen child that the UK doesn't know about might be able to get one, but in your case the UK knows about your child's nationality.
Your child can certainly enter Ireland with a Bolivian passport and then, assuming your child is a British citizen, can travel entirely legally to the UK without a UK passport or visa. In other words, yes, you can live in Ireland until the passport arrives, but you don't have to.