Couldn't a grandparent or other family member step in and make the sibling(s) their special priority for the time surrounding the event? I agree with the pp, that probably most doulas are in it for their special talent in helping birthing mothers and mommys/newborns get into their groove, and it would be quite a coincidence if they also were gifted at relating to older children and helping them have a great journey into welcoming a new sibling into the world. If there are no family members in your extended biological family who is up to the task, what about the child/children's godparents? Any adult they have a special relationship with already (like, your best friend, etc....)?
If only hired help is an option, then perhaps a temporary part time sitter/nanny/mother's helper who adores children and who clicks wonderfully with the sibling(s) in question, and is highly available to come by to help for some hours or full time during the sensitive time before/during/after birth?
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