With your Mum still alive, the situation is even more "odd".
Lisa, although you say your step mother doesn’t like you, would it still be worth asking her to sign the form?
You could fill it out and all she would need to do would be sign her name. With several marriages, I wonder if you would also need proof of divorce, remarriage etc? The plus side is that it if you go down this route it will not cost you anything to get the record.
If you wish to go ahead and try to obtain the record without your step mother’s input, I would still opt for adding a note - maybe something like “third wife still living” “lost contact” or “estranged”. That is truthful, and they can only say ‘no’.
It would be a lot more trouble for you to go through his third wife, and if the MOD are going to supply his record to her for free, they are likely to be more careful in checking entitlements I would imagine? Some people might try to deceive to save the £30, so you would expect checks to be made, especially as there are fewer and fewer wives of WW2 servicemen still living and a wife applying for a service record from WW2 might stand out. (This is just guesswork - I have no knowledge of the process)
I feel that their nok list is a bit unfair and children have just as much right to the record as a wife, but there is probably some logic behind that.
The situation is probabaly a little different here (Australia), but I applied for my grandfather’s unclaimed WW2 medals. My aunt, his daughter was officially nok though I had lost contact with her. I included a letter telling them this and the medals were sent to me.
Their list of nok was bizzarre in my opinion - I can’t recall the full list as it was some time ago, but quite remote relatives came before grandchild, such as sons and daughters of his siblings. I had no clue who they might be, and far as I know they would be all dead anyway. Grandchild was quite low on the list. I was quite upset by this at the time because I spent a huge amount of time with my grandfather, and as there was never any mention of nieces and nephews and I am sure he would have been miffed if any of them had applied.
I would say you should still apply for your father’s full service records.
Let us know how you get on if you decide to go ahead with it.