Seems to be a minhag that a fiance shall not sleep at his future in-law's house. Even just as a guest for one night. And obviously, even if there is no problem of yichud.
Is there a reference in posqim about this minhag?
This opinion comes from the Rama in EH 55:1, and Rav Soloveitchik was makpid on this (Nefesh HaRav pg.255).
Text of Rama:
הארוסה, אסורה לבעלה מדברי סופרים, כל זמן שהיא בבית אביה; והבא על ארוסתו בבית חמיו, מכין אותו מכת מרדות.
הגה: ואפילו ביחוד אסורים; ולכן ארוס שהוא עם ארוסתו בבית אחד, מברכין שבע ברכות פן יתיחדו (מרדכי פרק קמא דכתובות). ויש אומרים דאין להם לדור ביחד, שמא יקוצו זה בזה (כל בו). ואפילו בשדוכין בלא ארוסין יש לחוש (חדושי אגדה פרק קמא דכתובות).
Translation of Rama: even to be secluded is forbidden. Therefore,a couple that are engaged (eirusin) who are living together in same house should say sheva brachos lsat they come to seclusion. There are those who say they should not live with each other because they may come to loathe each other,even during engagement(without eirusin) one should worry about this.
Further clarification from Rama in his Darkei Moshe:
Writes that it's not coming from an issur standpoint ,but rather from the idea that they shouldn't get into the situation of coming to dislike each other(more of advise). However ,the Aruch Hashulchan 55:1 does bring this same idea,but adds that it can also lead to issur,and advises that if one is a Yirei HaShem they should avoid this and all other types of situations.
Text of Nefesh HaRav:
Translation of Nefesh HaRav:
Many times a bachur would come for a shabbos in Boston where his kallah-to-be lived. He would go to his future in-laws for shabbos,and Rav Soloveitchik would remind the bachur to be careful not to hang around(I understand it as sleeping) at night in the same house of his in-laws like the opinion of the Rama.
Further reading: See Shu"t Maharai Weil siman 55,and Nitei Gavreil Yichud Siman 49:13 that a single boy and girl should not reside in same residence even in a situation where yichud is not an issue since many problems can arise.
I can see two sources in the talmud:
A. Avodah Zarah 58b
מאי א"ל אסור משום לך לך אמרין נזירא סחור סחור לכרמא לא תקרב
Rabbi Asi repeated his question: What is the halakha? Rabbi Yoḥanan said to Rabbi Asi: Although the gentile did not touch the wine when diluting it, it is prohibited by rabbinic decree due to the maxim: Go, go, we say to a nazirite, who is prohibited from drinking wine and eating grapes; go around and go around, but do not come near to the vineyard. Although a nazirite is prohibited only from eating produce of the vine, he is warned not even to come into the proximity of a vineyard as a protective measure to ensure that he will not transgress this prohibition. So too, in many cases, the Sages decreed certain items and actions to be prohibited because they understood that if people would use them, they would eventually transgress Torah prohibitions.
B. Bava Batra 98b
גמ׳ למה לי למיתנא בית חתנות לבנו ובית אלמנות לבתו ליתני בית חתנות לבנו ולבתו ובית אלמנות לבנו ולבתו מלתא אגב אורחיה קמ"ל דלא דרכא דחתנא למידר בי חמוה
GEMARA: Why do I need the mishna to teach specifically: A bridal house for his son, and: A widowhood home for his daughter? Instead, let it teach: A bridal house for his son or his daughter, and a widowhood home for his son or his daughter. The Gemara answers: It teaches us a matter in passing, that it is not the proper manner of conduct for a son-in-law to live in his father-in-law’s home. Therefore, it is the father of the groom who generally provides a bridal home for the couple and the bride will return to live near her parents’ house only if she is widowed or divorced.
כדכתיב בספר בן סירא הכל שקלתי בכף מאזנים ולא מצאתי קל מסובין וקל מסובין חתן הדר בבית חמיו וקל מחתן אורח מכניס אורח וקל מאורח משיב דבר בטרם ישמע שנאמר (משלי יח, יג) משיב דבר בטרם ישמע אולת היא לו וכלמה:
Support for this is as it is written in the book of ben Sira: I have weighed everything in the pan of a balance scale and I have not found anything inferior to bran; but inferior to bran is a son-in-law who lives in his father-in-law’s house; and inferior to a son-in-law is a guest who brings in a guest; and inferior to a guest is one who answers a matter before he listens. As it is stated: “He that gives an answer before he listens, it is folly for him and a disgrace” (Proverbs 18:13).
וברוצים פנוי ופנויה להכיר זה את זו לתכלית נישואין אם ימצאו חן אם רשאים לשכור שני חדרי לינה בבית אחד שגם בעה"ב ואשתו דרים שם הנה אם יודיעו זה להבעה"ב ואשתו שאינם איש ואשתו יש להקל אבל כשלא הודיעו להם שאפשר שיחשבו שהם איש ואשתו לא יועיל ואסור אף ששכרו חדרים מיוחדים שהרי לא ישמרום ולא יתביישו מהם להתייחד וכדומה
And if a bachelor and a bachelorette want to get to know each other for the purpose of marriage, to see if they find favor [with each other], as to whether they are permitted to rent two bedrooms in one house where the owner and his wife live there — if they inform the owner and his wife that they are not married then we can be lenient. But if they do not inform them, such that it is possible that [the owner and his wife] will think that [the bachelor and the bachelorette] are married, it does not work. And it is forbidden even if they rent separate rooms, because they won't guard them and they wont be embarrassed of them to seclude and the like.
While not specifically discussing the future father-in-law's house, this shows that R. Feinstein did not think it was a problem for a boy and a girl who are not yet married to sleep in the same house, provided that they make it clear that they are not yet married.