Are Alyxia and Anemopaegma in the same family of plants?
no
Anemopaegma
Anemopaegma is a genus of flowering plants in the family Bignoniaceae.
 Species of Anemopaegma along with many other unrelated plants go by the name of catuaba.
Alyxia
Alyxia is an Australasian genus of flowering plant in the dogbane family, Apocynaceae.
 It contains at present 106 species, but "Alyxia stellata" and "A. tisserantii" are very variable, might be cryptic species complexes, and are need of further study.
 It consists of shrubby, climbing or scrambling plants.
 This genus occurs in China, the Himalayas, Southeast Asia, Malaysia, Australia, New Caledonia and the Pacific Islands.
 There are 14 species in Australia, 21 in New Caledonia and 7 in the other Pacific Islands, including Hawaiʻ i.
Urera kaalae
Urera kaalae, opuhe, is a species of flowering plant in the nettle family, Urticaceae, that is endemic to the island of Oʻ ahu in Hawaii.
 It inhabits slopes and gulches in mesic forests at elevations of 300 - .
 Currently it is restricted to the southern and central parts of the Waiʻ anae Mountains.
 Associated plants include maile ("Alyxia oliviformis"), hame ("Antidesma platyphyllum"), "Asplenium kaulfusii", "Athyrium" spp., ʻ āwikiwiki ("Canavalia" spp.)
, pāpala ("Charpentiera" spp.)
, ʻ akoko ("Euphorbia" spp.)
, poʻ olā ("Claoxylon sandwicense"), ēlama ("Diospyros hillebrandii"), "Doryopteris" spp., ʻ ieʻ i.e. ("Freycinetia arborea"), manono ("Hedyotis acuminata"), "Hibiscus" spp., olopua ("Nestegis sandwicensis"), māmaki ("Pipturus albidus"), hala pepe ("Pleomele" spp.)
, ʻ ālaʻ a ("Pouteria sandwicensis"), kōpiko ("Psychotria" spp.)
, heuhiuhi ("Senna gaudichaudii"), aʻ iaʻ i ("Streblus pendulinus"), ōpuhe ("Urera glabra"), and maua ("Xylosma hawaiiense").
 It is threatened by habitat loss.