No, a proton cannot be separated into two up quarks and one down quark. The stability and structure of protons (and other baryons) are governed by the strong nuclear force, which is mediated by particles called gluons.
The proton is a type of baryon, composed of three quarks. In the case of a proton, it consists of two up quarks (u) and one down quark (d), which gives it a net positive charge. The strong nuclear force binds these quarks together to form a stable particle.
Quarks are elementary particles and cannot be observed in isolation due to a phenomenon known as confinement. The strong force becomes stronger as quarks are pulled apart, making it increasingly difficult to separate them. As the separation distance increases, the energy stored in the gluon field between the quarks increases as well. At a certain point, the energy is sufficient to produce new quark-antiquark pairs from the vacuum, resulting in the creation of new hadrons (bound states of quarks) and preventing the separation of individual quarks.
This phenomenon is known as color confinement, and it explains why quarks are always observed in combinations that form color-neutral particles, such as protons, neutrons, and mesons.
Therefore, while individual quarks exist theoretically, they are always found in bound states and cannot be isolated or separated from the particles they compose under normal circumstances.