The current dynasty system is an interesting idea, but seems about half way to what it could be.
Current issues:
Unable to remarry with the death of a spouse. This can frustratingly end a portion of the game quickly for many players.
The age counters. This has been brought up multiple times. Instead of a numerical count perhaps simply 'Child' 'Young Adult' 'Adult' and 'Elderly' would work. Drives the point home about ages without strange situations of a 26 year old sovereign and 20 year old son.
Suggestions for improving the system:
Adoption-
Being able to bring in a hero as part of the line of succession and family. Adopted members have lower value when inter-marrying for dynasties.
Character perk changes-
Currently 'ugly' exists and it lowers the chance for offspring. It would make more sense for ugly to change the value multiplier for marriage, meaning that it requires more prestige to marry.
In trade, I'd suggest a few perks-
Infertile (lower chance for offspring)
Sterile (no offspring, must adopt)
This tweak to the system could allow for more interesting sovereigns such as a charismatic ruler who easily marries but can't continue their own dynasty and has to adopt their best generals into the family to marry with other factions.
One other issue, which has been brought up:
Use lines of succession as a game option.
ex. 'sudden death' games when setting up the initial rules are how Elemental currently treats sovereigns- once they die the game is over.
Games not using that setting, when the sovereign dies moves on to treating the next in the line of succession as the sovereign. A faction wouldn't be wiped out until all members of the line of succession have been killed.
This allows for more strategic/dynastic warfare where you might intermarry to remove a threat, hunt down the young nobles down the ladder, and finally when facing the sovereign you've weakened or eliminated their family line.
Some civilizations allowing for plural marriages (some of the Empires perhaps) could also add a twist to the entire dynamic.
