"Sometimes, the trees do not let us see the forest."
Translation:A veces, los árboles no nos dejan ver el bosque.
This is an established idiom in English, too.
"permítannos" is the plural formal command. So, you're addressing a group of people formally, saying, "Please let us [do whatever].
If you want to use permitir, it's, "A veces, los árboles no nos permiten ver el bosque."
But I think using permitir with trees is a little weird. Permitir carries more of an explicit feeling of agency on the part of its subject, whereas dejar is more comfortable in the context of something being blocked by an inanimate force.
The subjunctive (expressing counterfactual or uncertain situations) and imperative (command) forms swap the vowels. "Permitan" would be the 3rd-plural (or 2nd-formal-plural) subjunctive of permitir, which also gets used as the command. When you're in imperative, pronouns (me, te, lo / la / le / se, nos, os, los / las / les / se) get tacked on to the end, rather than stuck in front.
This is something you can optionally do sometimes with infinitives. With positive imperatives, it's mandatory. Though when you switch to a negative command, the pronoun moves back to the left. Nobody's ever given me a satisfactory answer as to where the hell that feature of the grammar came from.
Anyways, here's an example of using the imperative:
Por favor, señores, permítannos ver el bosque. Please, sirs, permit us to see the forest.