I've done this 5 times and my children are ok! Their ages range from 20 to 11. if you have air freight allowance / business class luggage allowance, try to take some familiar toys and books and items to keep them happy in the early days until the sea freight comes. Also car seats etc.
Before leaving use the web to look up clubs and activities you could sign up for to begin immediately. Use the school for help and information. Ask and be proactive.
Definitely be on the school run. it is the best (only) way of making friends. take the 4 year old with you. She is part of the experience and can make friends too. Be friendly at school and say yes To all activities and invitations in the early days. Otoh, don't get too exclusive with a small group of people immediately until you know them a bit better as extricating oneself can be tricky. Be pro active and invite a friend round for them from the very first week. Offer the parent a coffee/wine and a chat.
Don't be too hard on yourself. It takes time and you cannot speed the process as much as you would like. Just tell yourself and accept that it will take 3 months to feel your are finding your feet and at least as long again to feel the slightest settled. You just have to sit this out.
Accept there will be a honeymoon period followed by a dip. It will pass. Give yourself time.
When you miss things at home, or worry about what your children have lost, look at the things you have/experience that you cannot at home.
The experience builds resilience, flexibility, resourcefulness and cultural sensitivity in you all - fabulous qualities to have.
He children are young and will settle fine. Accept they might want to come into bed with you a lot or display other signs of insecurity. I would go along with it all. It all passes.
Good luck