What function is used to graph the potential curve of two hydrogens with parallel spins?
I believe that you wont be able to find a closed analytic expression for $\mathrm{H_2}$, since no closed analytic expresion is possible for a many-body problem (more than 2 bodies). That said you can calculate as many points on the triplet curve as you like by using a QM program able of doing unrestricted Hartree-Fock (UHF). Here you should be aware that UHF does not give very good potential curves, because the Hartree-Fock approximation lacks the electron correleation energy. $\mathrm{H_2}$ is a quite small system, so you will be able to make a potential curve using unrestricted MP2 or unrectriced CCSD. I do believe that PySCF is capable of doing such calculations. Regarding the experimental data, I am not aware of any databases for such kind of data. I would suggest finding a paper where a curve is presented and then use engauge digitizer to extract the points you need.