Cells can spatially and temporally control biochemistry using liquid-liquid phase separation to form membrane-less organelles. Synthetic biomolecular liquids offer a means to study the mechanisms of this process, as well as offering a route to the creation of functional biomimetic materials. With these goals in mind, we here examine the partitioning of long double-stranded DNA linkers into a liquid composed of small DNA particles ("nanostars") whose phase separation is driven by base pairing. We find that linker partitioning is length-dependent because of a confinement penalty of inserting long strands within the liquid's characteristic mesh size. We quantify this entropic-confinement effect using a simple partitioning theory and show that its magnitude is consistent with classic Odijk pictures of confined worm-like chains. Linker partitioning can also lead to inhomogeneous structures: long linkers excluded from the liquid interior tend to preferentially accumulate on the surface of liquid droplets (i.e., acting as surfactants), while linkers forced at high concentrations into the liquid undergo a secondary phase separation, forming metastable droplet-in-droplet structures. Altogether, our work demonstrates the ability to rationally engineer the composition and structure of a model biomolecular liquid.