Yes, lets count everyone getting there stuff as a short rest.

Ok

Garenlend opens up a bottle of wine and drinks half of it in one drink.

How long will it take to get to the kingdom with the horse and wagon?

1 day and 8 hours, when Garenlend was talking he meant by wagon and horse.

Ok and you said there was a government checkpoint we have to go through.

that took one hour to go through due to a very long line, so yeah I said that.

''Ok tell me when we arrive.'' Hoarah says going back into the wagon reading all of his wizard books.

Garenlend doesn't respond as he continues drinking the wine.

he then teleports back to the bar (mildly drunk) and then tells Delilah and Thomas to get their stuff and come outside.

Pac looks up from the ice pack and then walks over to the wagon. "My only request is that when we get there I need to buy some common clothing. Might need to steal some if it comes to it, but for right now I just need to sleep this off"

Garenlend hiccups, then grunts and says "Alright, just don't spill any water, I don't want any rotten wood on this wagon."

Garenlend travels 100 miles before stopping to rest.

Hoarah travels 100 miles before stopping to rest.

Garenlend hops off the wagon, grabs a wine and sleeps on the ground of the forest, oh right by the way you are in a forest.

Pac pulls out their bedroll and sleeps as well. Does this count as a long rest?

Yes

Hoarah continues to stay in the wagon and sleep.

Make a perception check please.

All of us or?