My mum always called her stepmum 'Mary' as her dad was widowed when she was a teenager. Mum was running the house at the age of 14. She taught Mary most of what she knew after her dad remarried as Mary had never left home and still lived with her parents 'til she married my Grandpa. However Mum's younger brother, who was a toddler when their mum died, called Mary 'Mum' despite having spent much of his very young life with his aunt while his mum was dying.
We called her 'Nana' and my children called her 'Great Nana' We always understood that she was not a blood relative but that didn't make her anything less, just different. Her dad, who lived with them in his later years, was 'Grandpa Webster'. The only reason we perhaps were less close to her was that she never had her own children, and she wasn't confident with children. We all adored her husband, my Grandpa!
When I became a granny I didn't want the title Nana as I associate it with someone who was slightly awkward around young children. Both myself and my DiL's mum wanted to be 'Granny' and my son said that was OK as we will just be Granny C and Granny H or possibly full surnames. Our grandson is too young to call us anything yet and he may choose to distinguish between us in some other way. At the moment all our contact is on video call as they live abroad, so we don't know if he has much understanding of who we are anyway. Hopefully that will change over the summer when they come to the UK for a few months, when he will be 9 months old +.
There are so many options for titles that I would imagine there could be a suitable one found that would be better than 'uncle' but the OP's DD has her reasons for not wanting her child to use ' Grandpa' and these need to be respected. Maybe suggest an alternative that would be acceptable to everyone.