We have hammocks for both vehicles and something like this is all that you really need. It will contain them to the back seat and prevent them from sliding off the seat into the floor and possibly hurting themself.

https://www.amazon.com/%EF%BC%BBUpgraded-Version%EF%BC%BD-Waterproof-Scratch-Backseat/dp/B07WFMH6FW/ref=sr_1_40?keywords=dog+hammock+for+car&qid=1674762488&sr=8-40

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My dog did ride better when crated though. When we traded trucks his crate would no longer fit in the back seat.

I bought this one

［Upgraded Version］ Dog Car Seat Cover for Back Seat, 100% Waterproof Back Seat with Mesh Window, Scratch Proof Nonslip Dog Car Hammock for All Cars, Trucks https://www.amazon.com/dp/B07WFMH6FW/ref=cm_sw_r_cp_api_glt_i_NM7DC12PAWV7R86BZHTK?_encoding=UTF8&psc=1 The reviews were all good except a few saying it’s not prefect water tight but I don’t really care about that as my problem is dog hair and dirt.

I like this one because it has the vented part up front so the AC can blow thru. It’s also got flaps to cover the doors if you care about that