Where was Jesus born?

A few years ago I heard an interesting sermon at a midnight service on Christmas eve suggesting that maybe we had got the Christmas story substantially wrong because of some bad translation and interpretation. It’s the kind of thing that makes you sit up and listen, because of the fact that it was someone I knew and respected standing up saying it I was intrigued. I have been doing some looking into it myself and there are some very interesting things that we read and miss both through our traditional understanding of the Christmas story but also reading the translations we have rather than looking back to the Greek (sorry I now sound all theological). I’m sure most of us are aware of things like the donkey not being mentioned in the story, although there is I suppose reason to think they may have had a donkey. But here are some of the other interesting things, there is no mention of how long Mary and Joseph had been in Bethlehem before Jesus was born, our nativity generally puts it that he was born the night they arrived, but lets be realistic, travelling 70 miles on foot or donkey when 9 months pregnant, I’m not sure. Next the innkeeper and stable are also not mentioned, in fact this is when if we go back to the Greek things seem a little strange. We are told that Jesus was laid in a manger because there was no room in the inn, but what if Jesus was actually born into a loving family home, this was the question put to us that Christmas eve. For years we have had this image of the stable (or for some a cave) because of the Manger (or feeding trough) plus the fact that we ‘know’ they did not stay at the inn. And it is the word ‘inn’ that is perhaps confusing, the Greek word is ‘katalyma’ which appears 3 times in the New Testament the other 2 are Mark 14:14 and Luke 22:11 both times referring to a venue for the last supper, an upper room or guest room which would be a more literal translation of the word. Think back to Jewish culture of the time, hospitality was a key thing, Bethlehem was Josephs ancestral home, there must have been relatives there. So what if Mary and Joseph arrive in Bethlehem and go to the family home, the guest room is already occupied possibly by older relatives, however there is a lower area where over winter and at night the families animals are brought in (this would also fit in with our understanding of Jewish homes of that period). Mary and Joseph stay in this lower area of a family home
At some time during their stay Mary gives birth and lays the Baby Jesus in the feeding trough for the animals in the middle of a loving family home?