This applies to England and Wales only; Scotland an Ireland were treated differently.

The Act for Better Observance of the Lords Day (1677) forbade all work and travel by horse or boat on a Sunday. The act was fairly seriously enforced at first, but after 1700, it lapsed somewhat. The Lord's Day Observance Act (1781), passed under the influence of the Evangelicals, forbade all forms of recreation on Sunday, but did not mention Sunday travelling.

The real problem with Sunday travelling wasn't the law, but the fact that people were supposed to go to church twice on a Sunday, and to fill the hours between the two services with contemplation. In other words, there was no time for travel. When Catherine first stays at Northanger, she is irked by the fact that the General insists that the time between the two services be filled with walking, so she cannot explore the house some more. She doesn't object to attending two services, however, and I think that as a rector's daughter, she would have been quite used to such activity. The General's punctilliousness about the Lord's Day observances when Catherine first arrives would have been picked up by a contemporary reader: presumably JA's comment about Catherine's being forced to travel on a Sunday is to show his inconsistent treatment of her, and to indicate that whatever it is that has vexed him has made him act in a manner not previously forseeable. I suspect that the contemporary reader would pick up the fact that the General is now behaving not only unreasonably, but in a manner directly contradictory to his previous actions. In other words, he's behaving like a gothic villain. And, of course, since Catherine will not have a chance to attend either Sunday service, she has probably emperilled her soul, given that a gothic heroine has life-threatening adventures whenever she travels alone! ;-)