I don't think either Dimon or to3d will flip every other volume, but you can do this with these commands. The 3dcalc command uses the flipped volume in every other TR. If you want the reverse, swap the a and the b in the expression. You can delete the AP flipped dataset.
3dLRflip -AP -prefix APflipped_all -overwrite epi_r1+orig.
3dcalc -a epi_r1+orig -b APflipped_all+orig. \
-expr 'a*mod(l,2) + b*not(mod(l,2))' \
-prefix epi_halfflipped -overwrite