Nagatoro and Chichibu in a day

What if I want to do Nagatoro iwadatami, hodosan shrine, Chichibu shrine and Hitsujiyama park in one day? Is that even doable?

That is easily doable even by public transportation, assuming you start and end your day in the Tokyo area. The following guide gives you access information:
https://www.japan-guide.com/e/e6550.html

You can buy rail pass from chichibu railway
Nagatoro chichibu outing pass=1600 yen