There is an allowance for a mobile caravan to be sited temporarily on agricultural land where essential for seasonal work which includes lambing.
There may be some issues tho which the council might raise which would probably include the following
Three sheep may not be held to justify invoking that exemption, as although you might say numbers don't matter where welfare is concerned, it is normally only used for large flocks where essentially a lambing stockman is working pretty much through the night lambing the ewes. Since sheep tend to lamb at dawn or a bit before and your house isn't far, they might say that it would be reasonable to get up early to check on 3 sheep.
Not saying I agree with that or dont agree with it, just second guessing them.
But they might just want you to provide them with the info that you have, so that they don't get it used as a precedent by other people, ie so they can point to the reasons why this is different to the normal rules.
In terms of you occupying it, the planning aspect rests on the usage and occupation ie you cant have any permanent occupation without planning permission. What qualifies as temporary would be defined by case law and also local council policies but 28 days is often used as a definition ie it has to be moved before the end of 28 days and sometimes not returned to the same location within 28 days.
Not a planner but have a caravan on a farm :-)