The problem is with interpreting Luke 2:7 rather than Luke 22:11-12.
The Greek word in Luke 2:7 that is commonly translated “inn” is katalyma. This is not the ordinary word for a commercial inn. In the parable of the good Samaritan (Lk 10:25–37) the Samaritan takes the wounded man to an inn. The Greek word in that text is pandocheion. The first part of this word means “all.” The second part, as a verb, means “to receive.” The pandocheion is the place that receives all, namely a commercial inn. This common Greek term for an inn was so widely known across the Middle East that over the centuries it was absorbed as a Greek loan word into Armenian, Coptic, Arabic and Turkish with the same meaning—a commercial inn.
Bailey, K. E. (2008). Jesus through Middle Eastern Eyes: Cultural Studies in the Gospels (p. 32). Downers Grove, IL: IVP Academic.
K. E. Bailey explains that, as typical of middle-eastern culture, Joseph and Mary went to stay with relatives, but the guest room was full. So, they stayed in the family room which had the manger at the end of the room.
For the Western mind the word manger invokes the words stable or barn. But in traditional Middle Eastern villages this is not the case.
(Bailey, p. 28)
See also In Luke 2:7 is "kataluma" a "guestroom" in a house or at an "inn"?
K. E. Bailey has a huge discussion on this. The first occurrence of Joseph and Mary staying in a barn/cave with animals was a novel 200 years after Jesus' birth.
The flaws with 'no room in the inn."
Joseph returned to Bethlehem because that's were his relatives were. They would offer them a place to stay. If the guest room was full, in the family room.
Joseph as from the family of David; thus a respected royal.
Their culture, as usual, gave special care to pregnant women.
Mary's relatives were also in a nearby village.
Joseph had time to arrange a place to stay.
The κατάλυμα is clearly in a house:
ἀκολουθήσατε αὐτῷ εἰς τὴν οἰκίαν
(in Luke 22:10, NA28)
ποῦ ἐστιν τὸ κατάλυμα (in Luke 22:11)
Thus, the upper room, was perhaps a guest room in a follower's house. Upper could mean uphill or second floor (up stairs). The BADG entry has the context suggests a dining room. One would think guest dining room since it was described as large and remote. A Pharisee would have trouble with the publicly, but a tax collector such as Matthew or Zacchaeus would be wealthy enough and not worry about image with the Jewish leaders.
The Son of Man has come eating and drinking, and you say, ‘Look at him! A glutton and a drunkard, a friend of tax collectors and sinners!’
(Luke 7:34, ESV)
And as Jesus reclined at table in the house, behold, many tax collectors and sinners came and were reclining with Jesus and his disciples. 11 And when the Pharisees saw this, they said to his disciples, “Why does your teacher eat with tax collectors and sinners?”
(Matt. 9:10–11, ESV)
κατάλυμα, ατος, τό (Polyb. 2, 36, 1; 32, 19, 2; Diod. S. 14, 93, 5; IG V 1, 869; Dit., Syll.3 609, 1; UPZ 120, 5 [II BC] al. in pap.; LXX; s. Bl-D. §109, 2; Rob. 151) inn. This sense is possible in Lk 2:7, but in 10:34 Lk uses πανδοχεῖον, the more specific term for inn. κ. is perh. best understood here as lodging (PSI 341, 8 [256 BC]; Ep. Arist. 181) or guest-room, as in 22:11; Mk 14:14, where the contexts also permit the sense dining-room (cf. 1 Km 1:18; 9:22; Sir 14:25).—PBenoit, BRigaux-Festschr., ’70, 173-86 (Lk 2:7). M-M.*
Arndt, W., Gingrich, F. W., Danker, F. W., & Bauer, W. (1979). A Greek-English lexicon of the New Testament and other early Christian literature : a translation and adaption of the fourth revised and augmented edition of Walter Bauer’s Griechisch-deutsches Worterbuch zu den Schrift en des Neuen Testaments und der ubrigen urchristlichen Literatur (p. 414). Chicago: University of Chicago Press.
In the Septuagint (LXX) κατάλυμα is generally used for lodging. (personal observation of 14 times used)
φάτνηa occurs only in Lk 2:7, 12, 16, and it may be important in some languages to distinguish clearly between various alternatives. The term ‘crib’ normally refers to the place where an animal stands when it feeds. The ‘manger’ is a relatively large box or rack containing hay, and a ‘feed box’ is a much smaller container, usually for grain. There is, of course, no way of knowing precisely where the baby Jesus was placed, but it would be very appropriate for the baby to have been placed in the feed box or in the manger. See also 7.64.
Louw, J. P., & Nida, E. A. (1996). Greek-English lexicon of the New Testament: based on semantic domains (electronic ed. of the 2nd edition., Vol. 1, p. 69). New York: United Bible Societies.