Well, Vervainkit and Milkweedkit are both very water-loving, so they sneak out of the nursery one day and go all the way to the lake to swim, but quickly lose control because, well at this point they're less than a moon old.
For some reason Rainfleck and Perchgorse are hanging out (Perchgorse used to be warrior, so maybe they're buds and go hunting together sometimes? Maybe Perchgorse needed someone to help her gather herbs and Rainfleck didn't feel like going on patrol? Who knows.) and they save the kits.
The kits say they don't have a mother (because Butterflyleap is nonbinary, so they aren't really a 'mother'), their clan scent was washed off from the water. And, because Milkweedkit looks exactly like Milkweedstar, and has the same prefix, they deduce that these kits must be Milkweedstars (his flirty ways have to catch up eventually)
So they bring the kits to their leader, and he is just as surprised as them, at least initially he is - he remember how he and Butterflyleap had grown close as friends, BUT Butterflyleap abruptly called off their weird friends-with-benefits/budding-romance out of nowhere a few moons back, without an explanation. Also, when Milkweedstar is mumbling while having flashbacks, he is trying to say he never had a mate.
Realizing Butterflyleap must have broke things off because they were expecting, Milkweedstar decides to keep the kits. He IS NOT doing it maliciously, but he knows that his deputy and medicine cat know both that these kits are his, and he doesn't want Butterflyleap to catch any flack or have their deputy position or reputation jepordised. Although, Milkweedstar is still pretty hurt that Butterflyleap kept the kits a secret from him.
AND SO Milkweedkit and Vervainkit grow up in Riverclan being raised by their father, forgetting about Skyclan, Butterflyleap and their siblings quickly because of their young age (Which isn't that far-fetched, because it happened to Mistyfoot and Stonefur too)
Milkweedstar, Rainfleck, Perchgorse, and Butterflyleap belong to @wc-grassroots