Totally disagree with this. Of course marriage does work like this sometimes but it doesn't need to - especially when it's a second marriage and nobody is sacrificing work prospects to care for shared children.
Everything being family money works when you only have children together and gives the primary carer the security and compensation they deserve for giving up or slowing their career and labouring with doing the principle caring and household management. It also works if one partner is the primary breadwinner while the other studies, raising their prospects to the shared financial benefit of the couple later. It also works because both parties are coming together often at the beginning of their economic lives, so they are largely building one financial vision together from a relatively similar shared baseline. basically, Each party are putting in something essential for the mutual benefit and shared vision of both of the couple, so 'what's mine is yours' works well.
However, in second marriages, you have an entire different set of assets and earning power coming into the relationship, that are a result of your labour/ decisions before the relationship. You also have a different set of obligations (debts, mortgages, children, family relationships and expectations) and quite likely different set of baked in financial habits. Particularly if you have no plans for further shared children, it's far less likely that one of you will be sacrificing earning power or putting more unpaid labour to the benefit of the couple as in a first marriage. It makes much more sense to take a fresh look at finances and work out what is actually fair.
Of course if one partner is super rich and happy to take the other partner and all their offspring on as dependants then lovely- but it's very 18th century and I'm not sure it's actually healthy for the relationship. (I think this is especially true when the man is the dependant, because it tends to erode their self esteem and sense of manhood). I think it encourages more unscrupulous people to marry as a meal ticket too.
OP, I don't think there is an easy answer to this. I'm in a very similar situation myself and I'm afraid it won't be just this that comes up as a question.... it goes to schooling decisions, housing, inheritance, everything....
My broad principles have been to make sure my partner contributes as close to his share as he reasonably can on costs, and that both parties should benefit from partnership. He is also committed to that and it's important to his sense of self esteem and my sense of not being exploited. His children are grown, but he provides for them when they need something, along with other family dependants he has. I step in in an emergency or when expenses are unmanageable, but he often pays me back when he can. He buys his own gifts for his loved ones and pays for maybe a third of our day to day dates. I 'treat us' both to luxuries that he could never afford- holidays etc.
We also have a prenup, so all my assets, including house we live in clearly remain mine and my child's inheritance. It is very much a win win situation, but NOT one that gives one person all the power and responsibility for finances or completely merges two very different lives.
He contributes a huge amount in labour - managing the house, car and garden in a way that makes my life way better, and his contribution to costs helps me as I'm not super rich. He lives in a property way beyond his means, including a work studio that allows him to develop his career and earning power in ways he never could have. He gets awesome holidays and splashes of luxury that I cover. But he (rightly) does not see himself as a dependant and remains ambitious about earning and managing his own money, rather than simply thinking that everything BraveGoldie has now belongs to him and his children!
His children are welcomed into the family, when they are with us, benefiting from everything we enjoy. But do I need to spend the same on them as my DD, or split her inheritance evenly between them all? No. I do build in money to spend on them and money to leave to them- but that's my choice, not obligation, and it's not equal to my dd.
Hope this is helpful.