We measured the magnetization $M$ of a twin-aligned single crystal of $\mathrm{Y}{\mathrm{Ba}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{x}$ (YBaCuO), with ${T}_{c}=91\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, as a function of temperature $T$ and magnetic field $H$, with $H$ applied along the $ab$ planes. Isothermal $M$-vs-$H$ and $M$-vs-time curves were obtained with $H$ applied parallel (\ensuremath{\Vert}) and perpendicular (\ensuremath{\perp}) to the twin boundary (TB) direction. $M$-vs-$H$ curves exhibited two minima below $38\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, which resembled similar curves that have been obtained in YBaCuO for $H\ensuremath{\Vert}c$ axis. Above $12\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, the field positions of the minima for $H\ensuremath{\Vert}\mathrm{TB}$ and $H\ensuremath{\perp}\mathrm{TB}$ were quite similar. Below $12\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, the position of the second minimum ${H}_{\mathrm{min}}$ occurred at a higher field value with $H\ensuremath{\Vert}\mathrm{TB}$. Below $6\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, only one minimum appeared for both field directions. At low temperatures, these minima in the $M$-vs-$H$ curves produced maxima in the critical current. It was determined that vortex lines were expelled more easily for $H\ensuremath{\Vert}\mathrm{TB}$ than for $H\ensuremath{\perp}\mathrm{TB}$ and, therefore, below a certain field value, that ${J}_{c}(H\ensuremath{\perp}\mathrm{TB})$ was larger than ${J}_{c}(H\ensuremath{\Vert}\mathrm{TB})$. At $Tl12\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ with $H\ensuremath{\Vert}\mathrm{TB}$, the relaxation rate for flux lines leaving the crystal was found to be different from that for flux entering the crystal. We also observed flux jumps at low temperatures, with their sizes depending on the orientation of magnetic field with respect to the TB's.