Thanks for the detailed reply.
If Cafcass aren't recommending a shared lives order, then the court would have to be persuaded of the benefits by dad's barrister.
Your situation is a classic lives with mum and spends time with dad situation. However, there is some recent case law to back the principle that even where the time split is weighted towards one parent being the main 'home', that labelling it a joint lives order can still be appropriate.
It will depend on the judge, as if they are very traditional, it's likely to remain labelled as you have suggested - lives with you and spends time with dad.
If they are younger, more influenced by case law, then they may go with joint lives.
In reality, it doesn't actually matter too much what it is called, it is the arrangements themselves that you need to have sorted.
Asa Cafcass say "up to six weeks holiday per year" why not propose a gradual increase up to that point as a way of him getting the six weeks but not until next year or maybe the year after?
If you can agree the contact arrangements then what the order is called is only a matter for short arguments or written statements before the court rather than a full final hearing.
I hope that this is helpful? Can I assist further at all?