Spoilers
About how trashoe knows that the baby is not his . He actually suspected that the baby is not his after he heard news of Navier’s pregnancy. But he actually thought that Navier is infertile because they both ate a cookies that contained infertility drug that was supposed to be given to the previous emperor’s concubine by the previous empress. So naturally he thought that Navier’s the one is infertile after all of their efforts. But after the news came , he thought that what if he’s the one who is infertile as Navier is having a baby right after she’s married to Heinley. Then , naturally he suspected that the baby Trashta gave birth to isn’t his . Soon he made a parental test (??) or something like a DNA test to see if the baby is his and negative is the result. By the way , Allen is the baby’s father . Both the first baby and the second baby who was for a moment became a princess are his . Roteschu is the father of Allen .
And that is about how he knew the baby isn’t his .
Spoiler
I don’t know about her babies but they said that she will commit suicide . Well , you’ll know later but when she gave birth after becoming the empress , she kinda went cuckoo . She threw her newborn baby on the floor . So when the news reached trashoe , he forbid her from touching the baby which is a princess. So trashta became wary of her position when she noticed that trashoe kinda lost interest in her. She wanted to use the baby to get closer to him but she can’t do that when she can’t even see her baby can she .
Do you need spoiler coz I will definitely spoil you! (=・ω・=)