My desire to talk about New Dream kids comes and goes, based on my current mood, but you fortunately caught me in a mood where I'm okay talking about it.
Rapunzel and Eugene's first child is adopted. They're an older kid, getting close to aging out of the system, with a chip on their shoulder because they're sure no one's ever going to want them. Basically, they find someone who was very much like Eugene when he was on the brink of becoming a thief. While I do not have a specific gender or name associated with this adopted child, the only time I ever wrote about them (in an RP) it was a boy named Gavin, so, for the sake of this post, that's how I'll refer to them.
Rapunzel and Eugene start "wooing" Gavin about a year and a half after she takes the throne (so not even right after they get married). They visit him weekly, bring him gifts, take him on outings, see if he's actually a good fit for their family. And then, they find out she's pregnant. Gavin is utterly convinced that this means they don't want him anymore, and starts getting closed off, but they ask him if he still wants to be a part of their family knowing that a baby's on the way. They leave it up to him. Stunned that they're still interested, he says yes, so they adopt Gavin before Rapunzel even starts showing.
Then it turns out that she's pregnant with not one child, but twins! A girl and a boy! The girl is named Claire and the boy is named Bastion. I've never thought too much about their appearances, tbh, but they're definitely both brunette, because I'm not fond of the headcanon that the Sundrop lingers in Rapunzel (or Eugene) and can be passed on to their kids. I also haven't delved too deep into their personalities. I like subverting expectations, but in the Tangled universe, how do you even do that?
While Gavin can never take the throne, because he's not of royal blood, he's the best big brother and protector the twins could hope for. Besides, it doesn't matter too much as Rapunzel begins to slowly dismantle the monarchy in her lifetime. While Corona never goes full democratic while she's alive (not that she didn't want it to, but everyone kept begging her to keep leading, so that was about as close to an election s se figured she'd get), perhaps within Gavin and the twins' lifetimes, it will be.