My mother's name is Barbara. She's 66, and she's always hated it passionately. It was seen as a bit of a naff name even when it was at peak popularity when she was young, and in her 66 years it hasn't come back around again even briefly, whereas names like Margaret, Mabel, Ethel etc. have had a little resurgence every decade or two before coming back with a bang.
My mum was teased horribly in her youth, and from then on she's been fighting a constant battle against people calling her Barbie, which she hates even more than Barbara. She always assumed changing her name was too difficult, but she's recently looked into it and found out it's not quite the nightmare she imagined, so she's seriously considering it. At 66. That should tell you how much she loathes it.
Honestly it's an ugly sounding name, and those don't tend to ever become popular again. For every 'old' name that comes back around, there's a half a dozen that have died off forever, and I suspect Barbara is one of those.
I think it would be a fine middle name though. You could still honour your relative, but if your daughter hates the name (which is highly likely, I've never met a Barbara who likes her name) she can avoid using it.