Peds is largely separate than adult palliative. While a pediatritian can complete an adult or peds HPM fellowship and go on to work a peds palliative job... someone that did one of the other ~10 gateway residencies is typically not going to be admitted to a peds HPM fellowship (example exemption would be someone that did psych and a child psych fellowship subsequently being eligible).
Hospice covers all age range and there is generally no particular "peds hospice" outside perhaps a children's institution happening to have their own hospice... say St. Jude's had it's own hospice. No idea if they do.
Whether you see peds patients as an adult palliative doc depends on the hospital culture and structure. If there is no peds palliative team, then it will likely be you.
Everyone does some peds rotation in HPM fellowship. I am EM trained so see kids in that setting. Many of the congenital issues and life limiting diseases of young children encountered during my HPM peds rotation in fellowship were novel to me. Eponyms galore. I would likely not be the best option for a peds team. I think the best primary specialty to take of the palliative needs of pediatric patients is a pediatrician with peds HPM training.
Otherwise everything is fair game when it comes to adult palliative jobs, assuming that they aren't looking for someone to function simultaneously as a hospitalist or geriatrician, etc (in which case IM/FM are likely going to be required).
So, yes, you can work in hospice coming from EM.