I've had a look at the Census for 1841 and 1851 (nearest censuses to your dates) but afraid I can't see any Rileys at all. Although the workhouse was quite big and visibly operating at that time the 1841 census isn't very clear about it - it does list lots of people in Brindle with no address - possibly workhouse inmates - but again no Rileys. The 1851 Census is quite clear about the workhouse and again no Rileys. Sorry.
This was a time when there was a lot of 'politicking' going on around the local workhouses about which should be the big one for the area - Leyland, Croston and Chorley were also in the picture. the minutes of the Chorley Poor Law Union are in the County Records Office and there are minutes about the time on Brindle Workhouse at the point you're interested in. I don't see any mentions of Riley in my notes, but I only transcribed ones about the operation of the workhouse, so it might be worth taking a look in case there's a mention of your family.
There definitely were children some children there, there is a guy in Chorley Historical Society who knows more about these than I do who is looking at how they charged the parishes of parents - I'll drop him a line.
This was a period when the workhouse was getting a little better - pleas had been made by local JPs to get it closed down because of conditions in 1826 - there's a fairly scary letter about this in the records office. By 1837, things were getting better and a year or two later it was rebuilt capable of taking 200 (though it never got that big again.) having said that, it was still pretty grim.
Despite not being able to definitely say the Riley(s) were there, it is quite possible they were but the records aren't available - it took people from all over the North West.
Sorry I can't give you any hard evidence, if I come across anything, I'll pass it on.
I've at least got a plaque on the site for those who died there as they would have been buried in unmarked graves. N.B. Not everyone stayed in the workhouse - it's quite possible they were there only for a time, especially if they wern't elderley or disabled.
All the best,
Bernard