Question: Although Tywin is Cersei's father, she is Queen Regent. Isn't she still in a higher place of power than him, and able to refuse to marry Loras?
Answer: The position of Queen Regent is largely a cipher as the Hand of the King is the actual regent for the king, handling day to day affairs and heading the small council. Tywin is still the leader of House Lannister and commands the army. Cersei's power derives from him, mostly. This is why she cannot truly counter Tyrion when he is acting Hand of the King or Master of Coin, both given by their father. She only starts acting like a queen when Tywin is dead.
Answer: As Hand of the King, Tywin is the second most authoritative person in Westeros behind only the king. The Hand's duties include sitting on The Iron Throne and dispensing order, justice and judgment, similar to what Ned Stark did in the Season 1 episode "A Golden Crown" while then-king Robert Baratheon was out hunting. It's also worth pointing out that Tywin's enormous wealth makes him the de facto most powerful person in Westeros, which he demonstrates in the Season 3 episode "Mhysa" when he sends King Joffrey to bed without his supper and remarks to Tyrion "You're a fool if you believe he's the most powerful man in Westeros. Do you really think the crown gives you power?"
Phaneron ★