If I understand this correctly, then you could...
1. Remove the dependency and place the NIGHTLY01 job in *HELD status.
That way, it stays on the job scheduler.
2. Then, add this as the last command for DAILYBACKUP:
SBMJOBJS JOB(NIGHTLY01 {grpName} {grpSeq}) TIME(*IMMED) DATE(*CURRENT)
...where {grpName} and {grpSeq} are filled in with the appropriate
values or *NONE as appropriate.
3. Add a new final group job for the MONTHEND group that contains this
same command.
Now, both jobs submit NIGHTLY01 when they need to.
Would that work for your situation?