I’ll be posting my drafts on 舊雜譬喻經 (T206), The Old Miscellaneous Parables Sūtra, a collection of stories with parallels in across the whole genres of KN, but mostly Jātakas.
I intent mostly the editorship of @cdpatton though anyone proficient can feel free to chime in!
Like my previous Therīgāthā Translation Questions thread, I hope it’ll be informative for students now and later, and prove to be an interesting documentation on pains and pleasures of translations! 
The first story is the #21, with the thematic parallel being Ja 436.
It sounds a bit misogynistic (well, blimey, perhaps it is); but there’s some nuances to it.
Although in both the stories, the women do not start off in a pleasant state - in Pāli, a woman kidnapped by the Asura demon is accused of adultery; in the Chinese, Asura demon is replaced by an ascetic who’s cuckolded by the woman he keeps hidden, and the jealous, possessive king’s chief consort flirts with the people. So there’s the interesting documentation of men trying desperately to kidnap women, and then accusing them of being unfaithful! Talk about the irony. 
This story is especially interesting because it has a well documented history of being part of the Daoist and then larger Chinese culture, so it’s an important piece of history to uncover.
Anyhows.
昔有國王持婦女急，正夫人謂太子：「我為汝母，生不見國中，欲一出，汝可白王。」如是至三。
Long ago, there was a king who kept his women under strict control.
The chief consort spoke to the crown prince:
“I am your mother! In all my life I have never seen the kingdom. You could inform the king that I wish to go out just once!”
Three times did she ask.
太子白王，王則聽，太子自為御車，出群臣於道路，奉迎為拜。
So the crown prince informed the king, and the king granted the request.
With the prince himself driving her carriage, the courtiers came out onto the road and bowed in homage to welcome her.
群臣: Not sure if “Ministers” is the right word, rather than “Courtiers”. Subjects? Chavannes has “Officials”.
夫人出其手開帳，令人得見之。太子見女人而如是，便詐腹痛而還。
The chief consort, putting out her hand, opened the curtain and let the people see her.
The prince, seeing a woman behave like this, feigned a bellyache and turned back.
夫人言：「我無相甚矣。」
The chief consort said: “How utterly unseemly am I!”
太子自念：「我母當如此，何況餘乎？」夜便委國去，入山中遊觀。
The prince thought to himself: “If even my mother is like this, what then of all the rest?”
That night he abandoned the kingdom and departed for the mountains, to roam and reflect.
時道邊有樹，下有好泉水，太子上樹，逢見梵志獨行來入水池，浴出飯食，作術吐出一壺，壺中有女人，與於屏處作家室。
At that time, there was a tree by the roadside, with a fine spring beneath it.
The prince climbed the tree and happened to see a solitary ascetic, coming to enter the spring’s pond.
The ascetic bathed, came out, and took his meal; then, working some magical art, he vomited up a jug.
In the jug was a woman, and in that hidden place, he played the husband with her.
作家室: Feels like a bit of playful wording for having sex. “Played house” or something like that?
梵志遂得臥，女人則復作術，吐出一壺，壺中有年少男子，復與共臥已便吞壺。
Then as the ascetic fell asleep, the woman in her turn worked the same magical art: She vomited a jug, and in the jug was a young man.
She likewise laid with him too, and then swallowed the jug back down.
須臾梵志起，復內婦著壺中，吞之已，作杖而去。
Presently the ascetic got up. Putting his wife back into the jug, he swallowed it down; took up his staff, and he was gone.
太子歸國白王：「請道人及諸臣下，持作三人食，著一邊。」
The prince returned to the kingdom and informed the king: “Invite the wayfarer, together with the assembled courtiers, and have a meal for three set aside.”
道人: I kinda like the sound of “Wayfarer” for the double connonations it has with Daoists and Buddhists both. Might be too bold a choice.
梵志既至言：「我獨自耳。」太子曰：「道人當出婦共食。」
Having arrived, the ascetic said: “I am all alone.” The prince said: “Wayfarer, you should bring out your wife to share your meal.”
道人不得止，出婦。太子謂婦：「當出男子共食。」如是至三，不得止，出男子共食已便去。
Unable to refuse, the wayfarer brought out his wife.
Then the prince said to the wife: “Bring out the young man to share the meal.”
Three times he pressed her; unable to refuse, she brought out the young man.
They shared the meal together, and then they departed.
王問太子：「汝何因知之？」答曰：「我母欲觀國中，我為御車，母出手令人見之。我念女人能多欲，便詐腹痛還。入山見是道人藏婦腹中當有姦，如是女人姦不可絕，願大王赦宮中自在行來。」
The king asked the prince: “How did you know this?”
He replied: “When my mother wished to see the kingdom, I drove her carriage. She put out her hand and let the people see her. I saw that women are prone to great desires, so I feigned a bellyache and returned. I entered the mountains and saw this wayfarer hiding a woman in his belly. Surely there was debauchery at work. So the debauchery of women cannot be hold back. I beseech the Great King: pardon the women of the palace, and let them come and go freely.”
姦: I think debauchery fits here, but I’m not sure.
王則勅後宮中，其欲行者從志也。
And the king decreed throughout the rear palace: Let her who wishes to go, follow her own will.
師曰：「天下不可信女人也。」
The Master says: In all the world, there’s no relying on women.
信: I wonder if I’m sugarcoating the “no trusting women” idea here. But given the context of the stories both, it seems reasonable to understand the meaning isn’t “Trusting” per se, but being able to hold / control / take up as a support for personal desires.
Apologies for taking so long to get to this.
What a difficult story. My first inclination is to consider it an allegory for fantasy relationships that people often harbor in their minds, which they think about in times of privacy. It would make sense of the metaphor is coughing up a jar with someone inside to have a relationship with. But the nested jars is a challenging thing to fit into that context. 
Overall, it is a good example of how men have treated women in the past as like children or pets, not people with agency. Maybe a woman doesn’t want to be in a relationship with you, sir?
Anyway - translation issues:
群臣 literally means “a group of ministers” - it’s pretty common as a term when a king is holding a discussion with his cabinet or advisors. In a monarchy, it would probably refer to his court; the officials who would give advise and execute decisions.
I think you may be right that 作家室 is a euphemism for sexual relations. Usually it refers to managing a family or home, such as the finances, etc. Here, it must mean they behaved like husband and wife.
道人 “man of the way” - refers to sages, ascetics, alchemists, etc. In a Buddhist context, “religious practitioner” is probably the meaning. Could be a Buddhist or non-Buddhist.
姦 definitely means something like debauchery, lewdness, etc.
I had a straightforward allegorical reading of trying to capture and hide an object of desire, but that thing always eluding and departing you - classical impermanence with a misogynistic dressing.
But yeah, nested jars makes it all the more colorful and weirder! 
