I have already replied, on the side of the dog isn't going to enjoy a trip to Brighton for various reasons.
The dog owner / your friend hasn't thought this through.
it wouldn't be advisable to muzzle the dog for the journey / the day as already said you can't just pop on a muzzle esp for a whole day, and I wouldn't muzzle an unknown dog in a car as it could be sick and that will cause problems on the journey.
The safest way for a larger dog to travel in a car is in a crate, I suspect the back seat of this car isn't going to be big enough for a crate ? and I suspect the boot of the car isn't big enough for a crate ?
I suspect the back seat isn't big enough for a crate and an adult too ?
I think the dog owner needs to accept / realise her life changed the day she adopted the dog and she needs to realise she needs to make different plans in advance - she probably doesn't want to leave the dog home alone for the day - it could howl / bark for the duration it is left ?
We don't know how long she has had the dog, nor if the owner works nor how long she works for and who, if anyone, cares for the dog whilst the owner is at work.
I have dogs ( plural ) I wouldn't arrange to go out ' for the day ' having recently adopted a rescue dog. but if I had to - i would be arranging dog care i.e. a dog sitter coming in / dog going to a dog sitter or even the dog going to kennels for the day or a family member having the dog for the day etc.