"Jenny does not want to go to the store."
Translation:Дженни не хочет ходить в магазин.
yeah should be correct. I'd say "не хочет ходить" means the person generally doesn't want to go somewhere (at anytime, any day).. like "my son doesn't want to go to school".
compared to "не хочет пойти" is more like someone doesn't want to do something in the near future (once) - like "my son doesn't want to go to school today" or "he doesn't want to go shopping right now"
I think идти is better here. Идти is a determinate motion verb (one direction) whereas ходить is indeterminate (multidirectional or habitual). If we use ходить, I might write the sentence this way: Дженни не хочет ходить в магазин каждый день на работу. This gives a "habitual sense" to meaning. But if we mean just one time, идти is the appropriate choice.
Think about the difference between:
Он ходит в школу. Meaning: he goes to school where he is a student; he studies, etc. The simple present tense in English is appropriate here.
Он идёт в школу. Meaning: He is going to school now, in the direction of the school, possibly for some purpose other than studying... maybe he isn't a student... maybe he's picking up his kid :) The present progressive verb tense is appropriate here: be + base verb-ing.
Он пойдёт в школу. Meaning: He will go to school. Future. Determinate. One direction for some immediate purpose. Does not mean he is a student. Again, maybe he will pick up his kids. Usually, the simple future in English is suitable here: will + base verb.
Он будет ходить в школу. Meaning: He will be going to school. Future. Indeterminate. Habitual. He will be a student. He will attend school in the future. Usually the future progressive in English works here: will + be + base verb-ing
Please do let me know if I've made any mistakes here. Thanks!