How is Pauli's exclusion principle valid for electrons of two hydrogen atoms in ground state, having same spin?

A quantum state includes the information about a particle's position. Two particles with the same quantum numbers at different locations are in different states, so are allowed by the exclusion principle.

1. You can't create two electrons with the same momentum, because you can't create even a single electron with a particular, exact momentum. You can create an electron whose spatial wavefunction contains an arbitrarily narrow distribution of momenta, but then the distribution over spatial locations will be very broad. Independent of this, if they are localized in different regions of space, then their spatial states are different.
2. Assuming the electrons in different H atoms are bound to distinct nucleii, their states will be distinct because of this. In principle, though, if we ignore the nucleii and just put a lot of electrons in a box at low T, we can get a degenerate Fermi gas in which the exclusion principle does matter. The situation is more complicated when nucleii are involved.
3. The spatial state of any particle is part of its state with regard to the exclusion principle, so no, two electrons in two different atoms are never in the same state. Often we focus on their atomic (orbital+spin) states, and people often just call these the "states," but with regard to the Pauli exclusion principle, the spatial state definitely also matters.