In the unlikely possibility you haven't seen Endless Waltz... be warned Spoilers abound...

Ms. Mariemaia Barton does not appear in the original GW Series.  Her first appearance takes place in the GW Sequel titled, "Endless Waltz".   With both her parents dead, Mariemaia was raised by her grandfather, Dekim Barton, one of the original men involved in the Operation Meteor Project.      Mariemaia is also related to the actual Trowa Barton, the original pilot of the Gundam Heavyarms before he was killed and replaced with the Trowa we now know.  The original Trowa Barton, was Leia Barton's brother, which would have made him her uncle.

It's unknown whether or not Treize was ever aware he had a daughter.  It is confirmed however Mariemaia was conceived during the period when Treize was injured in battle in space combat, where he met Leia Barton at a hospital way before he was the Oz Specials Commander.  

Mariemaia's mother: Leia Barton (or Lisa in the Toonami Version), was apparently a loving parent from the one picture they showed of her.  She unfortunately died only 2 years after her daughter Mariemaia was born.  From the picture Trowa (Leia's brother) showed to 'no name', Mariemaia and her mother and they were apparently very happy before her mother died...

It's possible Leia might have known about the plans for making her daughter "The Ruler" of earth. I thought this because of something her brother says:

"Her name is Mariemaia, she's my sister's daughter. She's going to be the leader of earth after we conquer it," --Trowa Barton, Leia's brother.

Maybe they made the plans for Mariemaia *after* Leia died, that's also possible because she died when Mariemaia was only 2 years old...

It's interesting to point out Mariemaia's unique looks.  She has red hair, whereas the majority of people in her family are blondes.  Leia - Blonde, Treize - Blonde/Brown, Trowa - Blonde, Dekim wasn't a blonde, but neither does he have red hair. 

With both parents gone Mariemaia was raised by her grandfather Dekim Barton who took advantage of her father's reputation and ideals to brainwash her, and make her the figurehead of the Barton Army.    Based on what Trowa said it's possible Leia knew about the plans her father had for her daughter, Mariemaia.

Dekim & Mariemaia turned their home, Colony X-8199, into a military mobile suit factory.  Following Dekim's plan they waited for the right time and abducted the influential Vice Foreign Minister of Peace, Relena Peacecraft. 

Mariemaia eventually takes on a new belief at the end of Endless Waltz when she decides to protect Relena Peacecraft from her grandfather and is shot.  After the war is over we see Lady Une pushing Mariemaia in a wheelchair.   Since that is where Endless Waltz ends it would be impossible to say what Mariemaia does after that point.  It's likely she was adopted by Lady Une and enrolled in a private school somewhere.