CGI looks fine to me. Did you guys expect the dragons to come through the screen and lick you, or something?
Rhaenys got to the Dragon Pit lost among the peasantry shephered there to witness Aegon's coronation. Presumably, there was no great need to guard the inner entrances as the frightened smallfolk would become crisp mince meat if they ventured down. Since the alarm hadn't gone up that Rhaenys had been broken out of her house arrest, there was no suspecting a rogue Targaryen in the crowd. Most likely Rhaenys knew she was outnumbered, alone and vulnerable, so had best break her dragon out ASAP rather than waiting and risking Aemond and Aegon chasing her down, the huge Dragonpit doors being closed, etc.
The real travesties there were her being uninjured by breaking through the floor & the smallfolk cheering Aegon as King.
As for the Baratheons, they had always been vocal defenders of Rhaenys' claim - her mother was a Baratheon. They also have Velaryon blood, in canon. It was fairly "obvious" they'd stand with the Blacks, until Borros' pride got the best of him and he didn't. Rhaenyra was stupid not to offer him a marriage or Council seat. That's kinda the point. But between Rhaenys and Lucerys patrolling the Gullet, Rhaenys was probably the better bet. It's a plot point Lucerys is making the shorter and (assumed) safer trip to deliver a simple message.