We consider nonlocal conductance effects in epitaxial trilayers made by ferromagnetic half-metal ${\text{La}}_{2/3}{\text{Ca}}_{1/3}{\text{MnO}}_{3}$ and high ${T}_{c}$ superconductor ${\text{YBa}}_{2}{\text{Cu}}_{3}{\text{O}}_{7\ensuremath{-}\ensuremath{\delta}}$ separated by an insulating barrier of antiferromagnetic ${\text{La}}_{1/3}{\text{Ca}}_{2/3}{\text{MnO}}_{3}$ with variable thickness. The Hall transresistance as a function of the barrier thickness and the applied magnetic field is measured to investigate the interplay between tunneling and frictional drag effects in ferromagnet/antiferromagnet/superconductor trilayers. The results show a subtle correlation between the tunneling and the drag to account for the observed decreasing of the transresistance as the barrier thickness and the magnetic field are varied. A phenomenological model addresses such features as an enhancement of the frictional drag when the process of tunneling gets suppressed.