Agree with trickle charging the battery for a week of nights before departing. Also prior to, do a before morning engine start voltage check across the battery posts for a week or so to see what the overnight battery voltage number is.Also take a good after market socket, breaker bar, and maybe an extra lug nut with you, for any unforeseen tire changes, I had one messed up lug nut, I guess the tire shop messed it up during the rotations.
The engine will normally start with 9 volts cold, but the battery should read closer to 12 volts and not less than 11.5 VDC.
If the battery shows low after a week of trickle charging, then maybe either the battery or the alternator is weak. The 3 has a way of masking problems and then just quitting with no warning. I see one of the alternator files in the link below has over a thousand downloads so maybe it is of some value. It is usually a problem with the internal "smart" regulator that talks to the car computer rather than the battery and hence at some point, the car computer just says - do not start the engine - something dumb like that - "not within design parameters" kind of computer logic.
https://www.disco3.co.uk/gallery/thumbnails.php?album=3801
As to the spare lug nut, yes, and I note that at some point one of mine got wrecked by I guess my independents air wrench as I change my wheels myself the hard way but the wheels are always coming off for some reason or other at the independents.