There is literally no way that the same house, in the same location can be called home by both Noble and Street Urchin.
I dont think this would be a problem to be honest ...
Where you started and where are you now are two different things. O_o
I mean ...
Look at Shadowheart, she is also an Urchin and she dont look any poorer than any other party member (maybe except Astarion).
On the other hand look at Wyll, he is a Noble (even tho his origin say "Folk Hero") and yet he isnt any wealthier than others (again, except Astarion).
I mean, origin of our characters can be litteraly everything between "this is what you did while Mind Flayers kidnapped you" to "this is what you has ben most of your life and what gave you your most valuable life lessons ... but its long gone".
Imagine a story ...
Boy, orphan, urchin, street rat if you wish ... had nothing, so he was selling himself for anything that would buy him something to eat ... one day he managed to get a job offering, delivering a message. After some time of delivering, he has ben offered by someone to be payd for telling what was inside the message ... and few dozen years later this boy become one of Kings advisers.
Does that ring a bell?
It should ... that is short story of Varis from Game of Thrones.
