LIN transceiver instability problem
I think it's VREG_OK that goes to 0

The problem is about the Vreg pin, but not about drawing a current from that pin. VREG_OK does not indicate if the Vreg pin is floating. Vreg is the output voltage of an on-chip regulator and the chip uses this voltage for the internals (look at the block diagram at p.2). It's not a must that you should draw current from that voltage.
However, this pin requires a bypass capacitor for stability (First sentence at p.9):

Img Src: Datasheet, p.19.
So, if you connect a low-ESR capacitor with a capacitance of at least 10uF then everything will be fine.

but if i disconnect Vreg from the Arduino that I power (just so it works, i don't need an arduino), it stops working. ... The arduino is just here so Vreg is not floating

Arduino's input line bypass capacitors are fixing the instability here :)