my dc's (both primary age) have clothes at both houses.
Uniform - 3 sets (though ds2 has lots more as we seem to have accumulated hand me downs). They wear a clean set to school, picked up by dad, that set stays there and is washed, wear a clean set the next day and come back here. I have 2 sets here for 4 days wear a week, so wash midweek.
If dad has them Fri evening they change out of uniform into home clothes before they go so that uniform doesn't accumulate there and they don't run out of home clothes. As they haven't worn those clothes for very long they usually wear them again the next day and come home in them that evening.
If he has them Sat evening they just go in what they have been wearing, change into clean clothes the next day and come home in them that evening.
They don't have masses at either house, so if either of us is taking them away we usually pass clothing over so they have enough shorts, trousers, t-shirts etc to last the time they are away.
Occasionally have a sort out when seasons change.
I buy the bulk of their clothes, as they are here more of the time, but dad does buy them some stuff. All clothes just cycle between the two houses depending - there isn't any returning to the house that brought it.
As far as I am aware they only have the coats and shoes they have here, they don't have any there, other than maybe wellies.
ds1 doesn't give a toss what he wears, ds2 will pick his clothes - but isn't bothered enough to say "where is that item" if it isn't there. Will see what happens when they get older and more fashion conscious.