Sharing some extra details to help me (and you) with any confusion!

The Targaryens are the owners of the House of the Dragon, the largest casino in Westeros, and they are incredibly rich.

Viserys Targaryen

Alias, The King
Role, Owner of The House of the Dragon
Marital Status, Married to Alicent Hightower
Children, Rhaenyra and Saera (With Aemma)
Aegon, Helaena and Aemond (With Alicent)

Daemon Targaryen

Alias, The Heir
Role, Co Manager
Marital Status, Married to Laena Velaryon
Children, Baela and Rhaena Targaryen (With Laena)

Rhaenyra Targaryen

Alias, The Spare
Role, Co Manager
Marital Status, Married to Laenor Velaryon
Children, Jacaerys, Lucerys and Joffrey (With Harwin)
None (With Laenor)

Saera Targaryen

Alias, The Princess
Role, None
Marital Status, None
Children, Viserys (Father Unknown)

Aegon Targaryen

Alias, The Joker
Role, Dealer
Marital Status, None
Children, None

Helaena Targaryen

Alias, None
Role, None
Marital Status, Married to Thomas Greyjoy
Children, Jaehaera, Jaehaerys and Maelor

Aemond Targaryen

Alias, The Brat
Role, Gaming Manager
Marital Status, None
Children, None

The Velaryons are the owners of The Sea Snake, another casino in Westeros, but it's not as large as The House of the Dragon. They are not competitors/rivals of the Targaryens since they married into the family.

Corlys Velaryon

Alias, The Boss
Role, Co Owner of The Sea Snake
Marital Status, Married to Rhaenys Baratheon
Children, Laenor and Laena

Laenor Velaryon

Alias, None
Role, Dealer
Marital Status, Married to Rhaenyra Targaryen
Children, None

Laena Velaryon

Alias, None
Role, Gaming Manager
Marital Status, Married to Daemon Targaryen
Children, Baela and Rhaena Targaryen

The Hightowers are literal leeches. They have managed to worm their way into the casino business without ever actually owning one. There is only one thing that people really know them for and that is the hotel that Gwayne owns, and the fact that they've married into the Targaryen family.

Otto Hightower

Alias, Hand of the King
Role, Part of the Board
Marital Status, None (Wife Deceased)
Children, Alicent and Gwayne

Alicent Hightower

Alias, The Serpent
Role, None
Marital Status, Married to Viserys Targaryen
Children, Aegon, Aemond and Helaena

Gwayne Hightower

Alias, None
Role, Owner of The High Towers (Hotel)
Marital Status, None
Children, None

The Strongs are the owners of the local library, Harrenhall. They do not factor into the casinos much (wink wink) and most of them work in the library itself.

Lyonel Strong

Alias, None
Role, None
Marital Status, None
Children, Harwin and Larys

Harwin Strong

Alias, None
Role, None
Marital Status, None
Children, Jacaerys, Lucerys and Joffrey

Larys Strong

Alias, None
Role, Janitor at The House of the Dragon
Marital Status, None
Children, None

Simon Strong

Alias, None
Role, Owner of Harrenhall Library
Marital Status, None
Children, None

Rhaenys Baratheon

Alias, The Queen
Role, Co Owner of The Sea Snake
Marital Status, Married to Corlys Velaryon
Children, Laenor and Laena

Other Details, Rhaenys is not related to the Targaryens in any way. She is a Baratheon who married into the Velaryon family.

Criston Cole

Alias, The Bull
Role, Security Guard of The House of the Dragon
Marital Status, None
Children, None

Other details, Criston Cole was hired by Rhaenyra when she saw him win a bar fight and he's now the security guard at The House of the Dragon.

Thomas Greyjoy

Alias, None
Role, None
Marital Status, Married to Helaena Targaryen
Children, Jaehaerys, Jaehaera and Maelor

Other details, He is not that important, but he's a good guy.

MORE DETAILS

Characters that do not exist and why, and characters that have changed:

Aegon III (does not exist for obvious reasons, Daemon and Rhaenyra are not married)

Viserys II (changed, is now Saera's son)

Helaena's kids (changed, are no longer Aegon's kids)

Rhaenys (changed, is not a Targ)

Laena Velaryon (changed, is still alive)

Addam and Alyn Velaryon (changed, are not Velaryons and work with Saera)

Alicent (changed, is basically the book version of Alicent)

Criston Cole (changed, is way more of a good guy)

Aegon II (changed, is not a prick)

☆☆☆

a/n- hope this helps.
also, I choose not to think about the family tree past Baelon