A pen does help taming Equus and can keep them from running into unsafe areas while you do, but you need to give them time in the game to calm down from being either dropped by a flyer or pulled by a lasso into the pen.

Once the Equus is in the pen leave it alone for an in-game day. Keep your tames and yourself away from the pen. Once it calms down, go in and tame like you normally tame an Equus.

be prepared to get Dizzy when taming the Equus

You can feed it then use a bola (which doesn’t lower effectiveness) and after that use fence foundations and walls to keep it in place and ride it for the duration of the tame. No need for it to run around randomly.

Xbox one: as soon as you mount you need to feed again straight away otherwise you're dumped.

FYI it takes 8 Carrots to tame not 4