Honestly, it takes ages for them to actually get divorced. But there's a reason for that since Sovieshu can't divorce Navier for no reason, he needs to gather "evidence". And on top of that, he never wanted to make the divorce a permanent thing. He wanted to remarry her after about a year. Aside from that, the lead up to the divorce shows Navier getting close with Heinley. Also, they get married literally minutes after Sovieshu divorces her, their wedding ceremony obviously happens later though. And what do you mean by "baby ting"?
The main reason Sovieshu wanted to divorce Navier was because he thought she was infertile. He thought this because when they were children, him and Navier ate some cookies he found which were laced with an abortive drug. The cookies were meant for one of the previous Emperors concubines by the Empress (basically Sovieshu's mother gave them to her husbands lover who was as apparently pregnant). Anyways, Sovieshu found them and together he ate them with Navier. Years later, after they were married they tried for years but couldn't have a baby. However, Rashta became pregnant soon after entering the palace, which lead him to believe that Navier was the infertile one.
Now, it's a huge deal if an emperor can't produce an heir. He can have babies with his concubine, but they would not be considered to be part of the imperial family, meaning they can't be an heir. By law, he needs to have a baby with his empress in order for it to be considered crown prince or princess.
Because of this, Sovieshu comes up with a plan to divorce Navier and 'upgrade' Rashta to be his empress so that when she gives birth, their baby would be the heir to the throne. He's not entirely stupid though, since he knows Rashta doesn't have what it takes to be the empress. So after a year, once the baby's position as heir has been solidified, he would remarry Navier to make her empress again since she is a good and competent ruler.
Yes, that's right. Navier overheard Sovieshu promising the Empress position to Rashta beforehand so she plans ahead by agreeing to marry Heinley if they got permission from the minister.
As for Rashta's 2nd baby, the father is her previous lover's. His name is Allen and he is the son of Rashta's owner when she was a slave. Allen is also the father of her 1st baby. Rashta also never cheated on Sovieshu with him, she in fact was already in the very early stages of pregnancy when Sovieshu found her.
Yes, Ahn (her 1st baby) is alive and well. He is living in Roteshu's home but Allen (the baby's father) is taking care of him. Until a certain point, Rashta thought her baby was dead until Roteshu told her otherwise and began to blackmail her.
Rashta does have plenty of misfortune coming her way, but they are rather big spoilers.
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Soon for becoming the empress, Rashta loses Sovieshu's interest and he starts being cold to her. There is this one newspaper reporter who hates her and always tries to find ways to bring her down in the media and more often than not he always manages to dig up dirt on her and reveal it to the public.
At one point Rashta also loses her only weapon - her beauty. She got into an argument with a maid who then retaliated by hitting her over the head. This left a scar on Rashta's forehead.
She also suffers from ptsd because not too long ago she thought Ahn was dead. Roteshu the bastard gave her a deceased baby and told Rashta it was her son. Because of this, she had trouble holding her 2nd baby Gloriem. Rashta decided to hold Gloriem while she was asleep, but since she was so calm and not moving she had a flashback to holding the dead baby. This lead her to get scared so she threw Gloriem to the floor. (Gloriem was fine since the floor was carpeted and she was wrapped in a thick blanket). As a result of this, Sovieshu didn't let Rashta see her for a while.
The only person she could really trust at this point was Duke Elgy. She makes him her concubine not long after she gets her scar. Unfortunately for her though, Elgy never truly cared about her. His homeland is the Western Kingdom (turned Empire) and together with Heinley they plotted to overthrow the Eastern Empire. They both had differing goals to each other though, since Heinley fell in love with Navier and didn't want to hurt her by hurting her motherland. So Elgy's tactic was to use Rashta for his own personal gain.
Over time, Sovieshu was gathering 'evidence' against Rashta so he could divorce her. This eventually lead to a criminal case against her. She was found guilty over a lot of things and I think she was either sentenced to death or life in prison. However while she was locked up, someone slipped a pill into her room. It was obviously poison and Rashta took it willingly. She died alone and her body was found about a week or two later.

Does anyone have any questions regarding spoilers they'd like to know? I'd be happy to answer (●'◡'●)ノ