I do wish sometimes people would actually look at the facts of the matter as they are being presented, rather than waffle on about OP being unsupportive, evil, or disinterested in her DD and GC, before they make sweeping pronouncements.
DD lives 1.5 hours away. A 3 hour return journey. She will not want to do that before and after a 12 hour nursing shift - that's 18 hours before she even starts to eat / sort kids / etc. How much will this fuel add to her cost of living - is this affordable?
The GC has high enough SEN that he needs 2:1 care, is at a specialist SEN school and has a specific transport bus laid on for him which gets him to / from the school at specific times of the day. This sounds like DD has got him nicely settled in, is dealing well with her local council and his educational needs are being met. She is not going to want this disturbed in any way. Who will ensure that the GC is there to meet the transport bus before and after school, as this will be from his 'normal' address and not the OPs? How does this work with the child being at OP's home 1.5h away?
The OP has children of her own, the elder can do some ad hoc childcare for their sibling but is in an exam year and this must take priority. The younger is still at the stage where they do need a bit of attention, plus they will be moving up to secondary next year and this can be a lot of change which creates its own issues. People suggesting that OP moves her own family (increasing the daily commute for husband - whether or not he is father to DD) at this stage in OP's family's life are unrealistic.
Nursing is well known for its anti social hours, and whilst I'm sure that the course will be as supportive as possible, DD will still have to do 12 hour shifts, night shifts, shifts in different locations etc, as well as the academic side of things (and you can't be expected to produce decent essays etc whilst looking after a baby and a high SEN needs child).
The one day a weekend, once a month, and 'some childcare' in the school holidays is probably fine, if that is what it is. But what are the childcare arrangements for the rest of the time? Who makes sure that the SEN child is there for his bus? What's happening to the baby? What happens to them once DD actually qualifies and gets a job? How does the DD study for the academics without some time to herself without them? I strongly suspect that this would expand, especially once the reality of the commute settles in.
The logistics and practicalities for this would mean a No from me before I even got onto the question on whether I'd like to do this or not - emotion or caring doesn't even come into it, you cannot just wing it for the next 3 years of studying and then into a job, on 1 day a month's agreed childcare. Huge stress, huge waste of time and money and it has been set up to fail from the start.
Unfortunately nursing is just not the right career path unless you have rock solid childcare arrangements, and back up alternatives for when these fall through. I am sure that there are other options for the DD which would be more realistic and pragmatic solutions, and which the OP would feel much more able to support.
It is also a salutary lesson in making sure that, if at all possible, you do the training etc for careers like this, with tricky training schedules, before you have children, as you will be in a much better position with much less commitment than after. Obviously it's a bit late for the DD in this case, and indeed for many others, but it is still easier to do it this way round.