I'm curious about this because I've seen it come up a few times in fiction, with both results. On Game of Thrones and Disenchantment (albeit the latter's a comedy) the implication seemed to be that the Regent still couldn't do anything against an explicit order from the King (ie Joffrey had Ned Stark executed against the Regent's wishes, and Odval was unable to have Bean executed without King Derek's guilty verdict).
On the flip side, Rome seemed to imply that no one took orders from an underaged King seriously (ie everyone just kind of ignored Ptolemy's ranting).
So, historically, could Regents overrule underaged monarchs? If not, then why bother with a Regent? Why not just let the advisors run all the stuff the King was too young to understand or care about?
As with all things that vary across centuries and spring up in very different societies . .
It Depends.
It depends on the age of the child, the legal code in force, the de facto political power of the regents, etc.
Obviously if a 4 year old monarch demanded something, they would be taken only marginally more seriously than I take my 4 year old.
On the other hand, Basil II Porphyrogenitus was crowned Basileus before his father died at age 5. Two generals were crowned and ruled as senior Emperor. Upon the death of the second, while Basil II was legally the senior Emperor, effective control of the administration remained in the hands of the eunuch Parakoimomenos Basil Lekapenus, who was the Great Uncle of the young Basil and the de facto chief minister. Basil did not come into his own until, when he was 30, he had Lekapenus arrested, stripped of titles and property, and exiled.
Louis XIII of France was 10 when his father was assasinated. By French law, he came of age at 13 which formally ended the regency of his mother, but she kept doing business as if he were a minor until he broke with her at age 16.
Some 600 years and 2700 km separate these two cases, But the key fact was a regency was always an exceptional case, and each regency was negotiated individually among the various powers that could exercise effective power. To generalize about Europe as a whole would be impossible, without addressing non-European legal systems.
Having not seen the HBO series Rome, I'm not sure which Ptolomy you refer to, although I guess Ptolomy XIV Philopater, who became Pharoah upon the death of his elder brother at age 12. The special circumstance here was that his brother had died rebelling against their sister Cleopatra VII who was at that point allied with the Roman Consul G. Julius Caesar. So there was a real ruler already in place, and one who had a delicate alliance to keep in balance. Had Caesar felt he needed to end the Ptolomaic line, it was well within his power. The appointment of Ptolomy XIV as Pharoah was a formality to comply with the Egyptian custom of having a male ruler. He died 3 years later, and is widely believed to have been poisoned by his sister. It is unlikely that, had he been foolish enough to defy his sister earlier, he would have been taken seriously by people who were well aware his sister could have them executed.
I decline to speculate on Game of Thrones, since it was not based on any actual historical practices. I will note that GRRM has claimed influence of the War of the Roses, and the most famous instance of regency during that time period was Edward V, who at age 13 became King. He was deposed less than two months later by his uncle. It is assumed, although there is no smoking gun at this distance, that he and his younger brother were both murdered on Richard III's orders.