If I had to guess… (IMO/MOO)
BK asked/insisted his father accompany him on the drive home by suggesting something along the lines of “the car’s acting funny, I need a new one, etc.” Remember, his father is in “maintenance” (per MSM) so possibly mechanically handy as well- if BK was ready to ditch the Hyundai, he could probably get more support from his folks by “demonstrating” something was wrong with it on a long, long cross-country drive.
What boggles my mind is how he was (presumably) able to act normal on that drive. IMO he’s cold-hearted enough to accept that IF/WHEN he is caught (I think he was feeling heat after the Elantra announcement,) he will have completely devastated his family. Sounds like money is somewhat tight- he had to know he’d require a lawyer at some point & there’s no way his family could afford a good one without putting themselves in serious financial jeopardy. Even if he thinks he can represent himself, he has to have studied enough cases to realize how poorly that generally turns out- a “good” attorney can likely be reasoned with to represent him to HIS OWN satisfaction. But those lawyers cost $$$, and it doesn’t seem like he was rolling in money at any time… (OTOH, he may allow a string of PD’s in order to claim “ineffective representation” and drag this out indefinitely, esp. if death penalty remains on the table…) He had to realize the publicity alone would be horrendous for them, even if finances were not an issue. Assuming they knew nothing (I personally believe at least his mother knew *of* the case if her public letters regarding Uvalde, abortions, etc. are true- she kinda/sorta follows the news) they will probably be wracked with the guilt of “should we have known/what could we have done”, etc.
MOO, his father may have jumped at the chance to spend that quality time on the road trip when BK suggested the car needed to be repaired/replaced. BK had to know that time together would be extremely uncomfortable (even if his Dad never heard about the crimes), but he was willing to “pay that price” in order to:
A) Get the vehicle out of the area (also probably realized it would be scrutinized/searched if left unattended for however many weeks over the break.)
B) Look less suspicious with another person in the vehicle if recognized.
C) Potentially use father’s CC to eliminate paper trail in case he was being tailed.
D) Have a quasi-alibi if questioned about leaving the area (“I wasn’t fleeing, I needed my Dad to help diagnose my crummy car and get it renewed in PA” or some such excuse.)
E) Confirm he’d done an adequate clean-up job (another set of eyes to point out dirty spots?)
TL,DR: I suspect once the Elantra details were released, he started to feel the heat & realize he was sloppy with his use of his vehicle. He needed it out of the area via a legit explanation- and bonus if he could replace it before returning to WSU. His poor family- I truly DO NOT believe they suspected him whatsoever. If it wasn’t for the Elantra tip-off, I think LE would still be digging (his DNA would likely get him eventually but the car flagged him, IMO.)
All JMO/MOO/speculation about that drive and getting his father involved.