Plenty of people work on their own – taxi drivers, truck drivers, snipers, paper boys. So being alone isn't an issue, but breaks are, and in some lines of work, like truck driving, they are not just on offer they are enforced
When I worked for a local authority we had a public venue (gallery) which was open of a saturday. It took one person to run if for the day, but I also had to work the saturday too simply so that they had some one to cover their lunch and two 15 minute breaks.
If its only part days being worked, or part of the day she's alone then that might be different.
regardless of legality it is a pretty stupid position for an employer to put someone in