Oh dear OP, that is a predicament and I'm not sure what I'd do in your shoes.
I'd like to let you know though that I had a very similar attitude to your daughter.
I was never fussed about marriage. Honestly thought it didn't matter to me. I hate surprises and being the centre of attention, and didn't think being married meant anything to me..
When my DP (now DH) asked my mum and dad's permission to propose (despite me being 42
)- they both thought I might say no. They knew I loved him fiercely but thought I may well prefer not to get married.
When DH proposed it was a complete, total, utter shock. The biggest surprise of my life. I was instantly over the moon, said yes, mumbled a lot of stuff and burst into happy tears.
It was a special moment, one I will always treasure- and would have been different if I'd known.
DP proposed in our hotel room, this worked for me as we were alone. I'd have felt very self-conscious in public.
Maybe you could ask DD's BF if he'd consider proposing somewhere private and tell DD that you compromised by making sure it was a private moment to make the surprise a little easier?