Had her father only ridden a little faster than the rest of the procession, Toria might have moved to try to keep up. However, she wasn't an expert on a horse. Not even remotely. Besides, there was a difference between riding and flying. Judging by her father's rapid dash through King's Landing atop his horse, Toria wasn't entirely sure that he knew the difference between the two. Nothing about this was reckless - her father was excellent on a horse.
Jeremy looked ready to try charging ahead, but a look from their eldest brother, Tymor, persuaded him to stay with the rest of the procession. That was just as well. None of the Lannister children were awful on a horse, but Jeremy lacked their father's control and quite possibly would run down the poor frightened stablehand.
Toria rode near the carriage where her mother sat with Septa Moyra, though even she had the urge to nudge her horse into a gallop when she saw the banners waiting to greet them. Her uncle, the newly crowned King, would be too busy to arrange for welcomes for each of the great houses. That didn't mean that they couldn't be arranged by their own families. The thought made Toria smile.
The remainder of the trip seemed unbearingly slow, but at last, she reached the stables, and dismounted with the aid of a polite stablehand.
"Allow me, my lady," said the young man, offering his hand so that she could get down more easily. Toria could dismount on her own, but took his courteously offered hand, and pressed a silver piece into it after she'd safely dismounted without getting any mud or dirt on her crimson dress.
Patiently, she waited for her mother and Septa Moyra, though she was still curious and continued to glance in the direction of the bannersmen who had all congregated here to meet them.