For present tense, it's really easy: There is no present tense for perfective aspects of Russian verbs. мыть is imperfective, помыть is perfective, so you can only use мыть here. You literally cannot use помыть to translate this sentence.
As explained in
Imperfective - Incomplete, ongoing, habitual, reversed or repeated actions
Perfective - Actions completed successfully.
When you're talking about present tense, activities have to be on-going. It doesn't make sense to talk about something going on at the present moment which has been completed and thus is not going on at the present moment.
The translation "The children are washing spoons at the moment". Isn't this also a viable answer?
Is the translation "the kids are washing the spoons right now" so with the added "right" an overstatement of "сейчас" or should it be allowed?
Your sentence is a rare example of possibility to make a word-for-word translation:
- The kids are washing the spoons right now.
- Дети моют ложки прямо сейчас.
"right" ("прямо") just emphasizes "now"