Ariel Young suffered catastrophic injuries after Reid -- a former K.C. Chiefs assistant coach and Andy Reid's son -- allegedly slammed his pickup truck into the back of a vehicle she was in on Feb. 4 in Kansas City.

Investigators say Young's brain was hurt badly ... adding she suffered a skull fracture and subdural hematomas, among other ailments, as well.

Young had been in the hospital since the accident trying to recover ... but her family said Tuesday she was taken home this week.

"Ariel is at home recovering," the family said in a statement, "we hope that her being in a familiar place will help her remember things."

"She is doing physical therapy but as of right now she still cannot walk, talk or eat like a normal 5 year old. Thank you everyone for your continued support."

35-year-old Britt was charged with one count of felony DWI on Monday over the wreck ... after officials say he had .113 BAC when measured around 2 hours after the crash.

Investigators also said Britt was going 83.9 MPH in a 65 MPH just seconds before the collision.

Britt surrendered to authorities and took a mug shot shortly after prosecutors announced the charge on Monday.