For everyone confused about the family relationship - admittedly, the drama writers didn't make that very clear, just giving us snippets of information here and there.
The Queen Dowager is NOT related to the current king, the two princes' father, so she is not their grandmother, let alone mother.
The king and his family
The king was first married to Yi Geon's mother, who died.  We saw the king visiting her grave when he was about to become king and move to the palace when the previous king was dethroned.
Then he married Grand Prince Do Seong's mother, who is the kind young queen, who raised both boys as her own.

The Queen Dowager (Su Hyeon) 

The Queen Dowager was forced to marry the father of the dethroned king. Initially she was only a "queen consort" or a concubine, not the queen, as we learned in episode 8.  Her husband was much older than her, and he surely already had one or more sons. One of those was the one who became king, who killed Su Hyeon's young son, Grand Prince Gwang Chang, his half-brother, who was still a boy. We saw the boy being dragged from his mother's arms in flashback, in episode 5. He also banished her in a secluded palace, where she lived in misery and resentment, bidding her time.
Why I'm saying she was a step-mother of the dethroned king and not his mother?
After all, we heard the present king saying, in episode 1:
"The deposed king you served banished his mother and murdered his younger brother. He was a tyrant and a foolish king, who sucked the lives out of his people,"
But I think that he uses "mother" loosely, and in fact the (now)Queen Dowager was his step-mother, not his blood mother. What am I based on?
See this conversation in episode 2, where Left State Councillor (the one with the different eyebrows) lectures his daughter the queen and grandson, Grand Prince Do Seong:
"Why do you think the queen dowager's son, Grand Prince Gwang Chang, died? The deposed king also was opposed to it. However, the southerners ultimately made him into a traitor and killed him. Would he have done so if he were his blood sibling? Just like the deposed king and Prince Gwang Chang, the crown prince and our prince Do Seong... are not of the same blood."
If the two sons of the king were not of the same blood, it means that the dethroned king was not her son. She had become the queen by now, so she sort of "served" as his mother, and he also probably called her "mother" but they were not related. Just as, now, she is not the mother of the present king.
By the way, our present Crown Prince Yi Geon (the ML), in episode 4, suggests that the young prince who was killed was not the king's son, but her lover's son:
"As it turns out, Prince Gwang Chang is mixed with the dirty blood of the man you had an affair with"
We still don't know about that. It's probably a baseless accusation, since her lover tells her that he met her again (and presumably resumed their affairs) after a long time.

Thus she had a deep grudge against her cruel step-son the king, who not only killed her son but banished her for 10 years in a secluded pavillion. She planned his death by poison, and had him dethroned, and put the current king in his place. That's why she tells him, in episode 2 "King,  I am the one who put you on the throne. Remember that I can also bring you down." And, a bit later,
"The deposed king. Because of that despicable man who deserves to be chewed up, do you know what I did while I was confined to the back garden palace for those ten years? I made sure everyone in the palace became my people. I kicked out whoever did not follow my order by coming up with whatever excuses and put one of my own people in that position.  With the sole aim to take revenge on the deposed king. And after that, do you know what I did? For a year, through the primary royal chef, I fed the dethroned king... a little bit of opium. And his original madness became even worse. I thought of using poison in case opium did not work on him, but that wasn't necessary after all."

In episode 4, the Left State Councillor tells his daughter and grandson:
"Do you know how the deposed king lost his throne?  If the queen dowager decides it, His Majesty can be dethroned at once, just like the deposed king".

The current king  was happily married for the second time and used to live outside the palace with his two sons. It is not specified, but he might be a distant relative of the royal family; a cousin or something like that, the next qualified heir to the throne. Be it as it may, with no blood relationship with the current queen dowager.
The queen dowager, after losing her son, is not blood-related with ANY member of the royal family, past or present.

I hope this helps. 

Thanks for doing this! Appreciate it! 

Nicely done!

The show didn't do a great job with this, but your explanations were great. Thanks. 👍