We're in CH but in the French part. Do you have your house/apartment in Zurich sorted yet? Have you been put in touch with a relocation agent in CH yet?
Once you have these sorted your next step is wrapping up your house in UK. You will probably be asked to find a number of relocation companies to quote for your move. I can recommend Crown, they are good. Your DH's company will probably choose the cheapest quote, what a surprise, so avoid getting a quote from a removals company that is not rated highly. When they come over to quote they will want to see and measure everything, including what is in the loft, so anything you don't want get rid of. Ear mark any expensive items of furniture and request that they are crated for the move, this will cost more but i have always struggled to get any kind of decent payout for damaged items in moves. A knock to an expensive Danish coffee table will ruin it but you will only get a small percentage of the cost in compensation because a knock doesn't make it unusable.
Day or days of the move are tough. Pack yourself and DCs enough clothes and toys to survive the duration of the packing, the period of the move when you will likely be in a hotel up until you are reunited with your boxes in your new house. I moved with a young baby and did the following - moved myself into a spare room in the house with baby and dog and everything we didn't want them to take because i was taking it myself and everything the foreman and myself had agreed would be packed at the last minute ie. travel cot and jumperoo and my bed. We were in prison in this room for a few days during the duration of the move but we had privacy.
Our foreman informed me a couple of hours before the trucks were finished packing that there was some space and advised me to take a trip to the nearest supermaket to stock up - nappies, wipes, the inside of those nappy bins, this all costs a lot more in CH than UK and we filled the remaining space up.
The removal comany will store your stuff until your new place in CH is ready for you to move in. I've spent this time in temporary accommodation and hotels. Make sure you pack for that.
You will arrive in Zurich in Jan/Feb there will be snow on the ground. DCs will need winter wear - snow suits and snow boots. Buy this in the UK in advance and save yourself a race to the shops upon arrival. A few other things you can do before leaving UK to save hassle on arrival are - get passport photos for all the family for your permits, get everyone's hair cut just before you go (took me a year to find a decent hairdresser in CH that didn't charge the price of a cheap holiday), buy some moving house presents for your DCs that will keep them busy during the unpacking period.
Good luck. Oh and don't forget your tea bags.