Hello Jemma,
You are partially right in your first thoughts.
Your van wil be covered by your car insurance whilst it is being towed, as long as you have informed your insurance that you have a caravan and wil be towing it.
However it will only be covered for 3rd party risks, ie for whatever damage it does to other peoples property in the event of an accident.
Similarly some of the contents may be covered by your house contents insurance if you have that clause or option available in your policy and have declared such items will be used outside the house.
In both cases do not assume it to be so, make absolutely cetain with your respective insurers.
As for the van insurance, legally yo udo not actually require any, strange as it may seem, but, and it is a BIG but, if you damage your own van, it can be very costly to repair, or if after you unhitch from the car, the van rolls off down hill and hits someone or something, it again can be very expensive to sort out.
For your own peace of mind, and th esafety of everyone else, it is highly desirable to have a good policy running to cover all eventualities.
The best and least onerous policies are offered by th etwo main clubs, the Caravan Club and the Camping and Caravanning Club, with other good and reputable companies also available, such as NFU, and others.
Be very careful if you look at cheap options as normally their restrictions and small print wil give them many ways out of paying up if you claim.
The CC and C&CC are very good, and quick to sort out claims as I can personally testify following having had to claim on 3 occasions, two were my fault, one after a break in and theft of equipment.
Look through the forum back pages to get an idea of what other folk recommend, the majority seem to use the CC or C&CC.
Whatever you think you may use, it is worth asking here if anyone has any information that can help you form a decision.