It sounds really hard. I feel for you (and your DD). I'm a single parent myself (no help from ex) and the juggle/struggle of trying to find childcare when you are doing shift work is very real (I'm an HCP working on an acute ward). In all the years I've been a parent, I have found just one CM that would do extended hours (06:30 to 20:30hrs), but I paid a huge amount for that, and kept it going for a year as it would have cost me more in the longterm if I had lost my prof registration. The nursery my DC went to covered 07:30 to 18:30. My shifts were 07:00 to 20:00.
Four years ago, I managed to negotiate so that I worked 08:15 to 17:30 on fixed days during term time. This was trialled for about 2-3 months, reviewed by management (and they said that it worked well, thank God), and I've been doing those hours since. I work normal shifts during school holidays (eldest is happy and able to safely watch youngest). My DC are now 16 and 10, so once the youngest is safely able to get to school and back independently/be able to be home alone for a couple of hours, I can go back to normal shifts during term time.
Moving away from the thread, I do think that there should be provision that covers shift work (the early starts and late finishes), because I know there are lots of us out there who work those shifts and are stuck. It gets me so cross that there is still such difficulty in getting robust childcare that covers shiftwork.
Forgive me if this has been asked already, but has your daughter been able to see if she could compress her FT hours into fewer days each week? That might make it easier? Maybe she and her DS could stay over at yours on the days she works, and then back to her place on the other days. I remember doing that when my parents were still here (they were happy for me to do that) and they'd do nursery drop off/pick up and school run. In return, I paid for a gardener and a cleaner for them. I also gave them housekeeping to cover the days we stayed there.