It will depends on your creatures physiology and behavior, but nature is plenty of symbiosis examples so let's speculate how to make this cohabitation plausible.
Despite their destructive tendencies, humans live side by side with many different mammalian species - cattle, cats, dogs, horses,... And it happens that we all have the same common ancestors - ancient mammals. But I'll take the guess that you are suggesting a much closer ancestor, eg as close at the one humans share with the other apes.
Something that is apparent in the domestication process, is that it is in the benefit of the dominant species - humans. We use dogs for guarding, cats to chase pests, horse to carry loads and move faster, cattle for food. There are some examples we domesticated monkeys to grab fruits, and nowadays monkeys are still used in medical research as a close example of human physiology.
Here, both of you species are dominant so each needs to get a benefit from the proximity of the other. You said that one is much bigger than the first one, which is an obvious advantages for bulk force works. The small species, in contrary, could be better suited for precision handicraft (eg as weavers, jewellers or blacksmiths). It also likely that your small species would be more numerous than the big one due to much lower food needs, thus for similar resources they would provide more brains and more hands.
In addition to make sure that each species would get an advantage from the other, you may want to reduce competion between these. For example, having your big species an herbivore and the small one an obligatory carnivore would prevent them to compete for the same foods. However, if they develop agriculture, fields for the cattle used by the small species would compete with the pasturages/forests required by the big species.
In our world, Sapiens humans interbred with other hominins so our current species share a few % of DNA with Neanderthals, Denisovans, and possibly others to be identified. In your setting, natural interbreeding would be impossible for obvious reasons - but maybe they could experiment with artificial insemination to create hybrids.
Having a close ancestor raise the question of the huge size difference between your species. Fortunately, we have real-life examples of species exhibiting unusual sizes when isolated on an island. Maybe a geological event isolated one of your species for a few millions years on an island, creating a giant/dwarf population which then expanded back on the continent.
A possible origin for this relationship could come from mutual protection. Maybe your world was a dangerous place in ancient times, and your small creatures required protection from their big brothers. On the other hand, while your big creature was well fitted for combat, they had difficulties getting rid of parasites that hanged on their tough skin. Your small creatures where happy to make a feast on these, and maybe this grooming tradition even perpetuated in their current society.
Who would hold the power in your society will largely depends on your creatures physiology, but it is likely that the smaller species would get an overwhelming advantage simply because they are smaller and then require less food. You could nerf this by making them dying much younger.