My working day is when I get to the office/yard, then set off from there to the job. The office is only 15 minutes away from where I live, which is handy. I get paid from the time I get to the office and then leave.
If I lived 2 hours from the office, then that's down to me to get there and back of course, like most 9-5 jobs.
If there sending you to various sites then its down to them to pay you for it. Picking up another working is something that you shouldn't have to pay for.
If travelling is part of the job, then its part of your pay! They sound like fuck wits.