As I was reading through my textbook, I got to know that in an orbital, there are 2 electrons of opposite spins. My question is: Shouldn't they collide whilst they are rotating?
While there is no perfect classical analogy, the spin of the electron is angular momentum, about its own axis, not a direction of rotation about the nucleus.
In comparison, Venus rotates about its axis in the opposite direction of Earth, but this does not make the planets more or less likely to collide.
In reality, electrons in a molecule are colliding all the time insofar as they are experiencing a force (the Coulomb force) due to the presence of other electrons, and are correlating with each other as a result. Orbital models like the Hartree-Fock mean field approximation mostly neglect these interactions, so the answer to your question is they don't because the model doesn't consider such dynamics. But many sophisticated methods for calculating the effects of this correlation exist. E.g. "Full Configuration Interaction" and "Density Functional Theory" are two such methods.
So keep in mind that orbital models are only approximate. It is fine for many purposes, but inadequate for many too. The true ground state wavefunction of a molecule cannot be represented by a single determinant, and therefore cannot be thought of strictly as a collection of electrons occupying orbitals.