Shaw is the Mother of the Xenomorphs

We can ONLY go and Speculate as to what had Happened.

The NUTS and BOLTS seems to Indicate that David had Experimented and Cross-Hybred a Number of Different Experiments... which Included the USE of Female Engineers.

But is seems that he Found that Dr Shaw's Body and most likely HER very Reproductive Organs had Yielded more Perfect Results...

The Indication is therefor that those EGGS in the Room that Oram was taken to had came about thanks to the Donation of Dr Shaws Body.  It is UNLIKELY that she had wanted to PLAY any Part in this.... it would seem that Dr Shaw had DIED some how, and then David had then thought about USING HER in his Experiments.

The Drawings of Dr Shaw, had been indicated as Possibly being Twisted Thoughts and Desires of David.

"It is her motivation to perhaps go along with David's plot or in his twisted mind, his 'gift' to her"

It had been Indicated by someone on SET that Dr Shaw had been HIDING away in the Crashed Juggernaught.  Looking at Various Clues.... i would CONCLUDE the Most Likely Fate of Dr Shaw is as Follows.

* David would have led Dr Shaw to believe some Accident had Happened that Caused the Ship to Crash and Contaminate the Planet.

* He would advise Dr Shaw to remain in the Ship while he would go out and Explore the Planet looking for Clues and the Extent of the Contamination.

* It is likely that Dr Shaw would require Food and Water, and Once Supplies were LOW on the Ship, David would bring her more from the Planet (his Notes show he had been to Water Bodies and Studied Plants and Water Organisms). And so he likely brought her Water and Food and made some Excuse to HOW they are NOT Contaminated.

* She would grow Suspicious of him as he would Disappear for Days on End, and its LIKELY she would One Day go and Follow him, and then Stumble upon the Experiments he had been Conducting on the Engineers.

* She would Confront him, and he would LIKELY suggest he did all this for HER and he was trying to Find a way so that she can Re-Produce so that eventually she could Re-Populate this World and make it a NEW EDEN.

* She would DECLINE and likely try to FLEE or ATTACK him, and then she would have LIKELY gone to Attempt to LEAVE in the Juggernaught.  But Failed.

* David catches her.... she eventually Dies or is Killed and then David goes to USE her for his Experiments... Resulting in those Eggs.

I wish that was shown in the movie

Well its Pretty Much Speculation by me looking at the Clues and what would make Sense.  I think that what had Happened during those 10 Years between Prometheus and Alien Covenant would have Warranted a Novel to give us the Answers... this would be MUCH CHEAPER than a Movie.

There are a LOT of Details within Alien Covenant and if we look into Davids Notes and the Time-Line... Details that are Overlooked or we simply have to IGNORE.

There are some who SIMPLY look at it that it took David like Years to get to Planet 4... and so WAY LESS than the Covenant Ship had done... REALLY?

Some look at it that this took David just Days from when he left LV-223.... but if you look at the Clues it indicates to me that David and Dr Shaw had gone back and Forth to LIKELY the Life-Boat to get Various Stuff to take with them, this would be done over the Course of a Day or so.....   The Dr Shaw Birthed Deacon (Via her Trilobite Child) had taken Days to Gestate and so they would have LEFT before then and David could tell Dr Shaw that the Engineer and the ALIEN that she had GAVE BIRTH too have both Died.

Looking at the Clues... it seems that David had Helped Dr Shaw to Leave LV-223 but then he had NOT shown her HOW to get to the Engineers World... it seems that it had TAKEN her Many Months out in Space Floating in the Juggernaught before David had Persuaded her to PUT HIM back together... and then that SHE would NEED to go into Cryo-Sleep for the Journey.

Both UNTOLD Stories are NOT something you could Execute in a Movie where you have just the TWO CHARACTERS for like 70% of the Movie.... but they are STORIES that could be TOLD in a Novel.