"I go here and there on the weekends."
Great example to show the intracasies of translation. The order of words might have been chosen to produce a more flowing and pleasing sound to the ears ... In Japanese "there and here", in English "here and there" ? Shame there is no built in explanation, but I guess that mimics real life. Try to say both あっちこっち and こっちあっち and see what you think.
This course is made by contributors who (as far as I'm aware of) don't work for Duolingo. Also, 2 years ago they didn't have a hearts system. I've made a second account to try the hearts system, and I gave up on using Duolingo after 2 days. I'm really glad that I don't have the hearts yet since that system is terribly discouraging. After all, it punishes you for making mistakes. Punishing people for their mistakes is a great way to make people uncertain about themselves and to make them really frustrated with the app.
The order also matters in other lessons, for example mother and father is sometimes marked as incorrect if you translate father and mother, I guess to make sure you understand which is which.
So even though あっちこっち is an expression, and the same expression in English reverses the order, it makes for a bad lesson in the rules of Duo.
こっち by itself is a pronoun but あっちこっち can be an adverb.
There is not supposed to be a と. It would probably not be idiomatic Japanese to have a と. Language structures don’t map 1:1 onto each other. Just because there is an “and” in the English sentence does not mean that there must be a と in the Japanese translation.