I'm pretty sure I don't really qualify as an ex-pat parent, when my mate drinking two year old barks orders at me in Spanish I wonder if there is anything English about him at all! This is because when he was born I had already lived in Buenos Aires for 6 years. However a recent trip to the beach gave me a fascinating insight into what it must be like for kids to make a huge change like moving to a different country. Just this small change of scenery was enough to change his behaviour dramatically (not in a good way unfortunately). People say that kids adapt really well to new situations and I think this is true but I also think that the emotional impact can be significant.
So what can you do? Most mental health practitioners that work with children agree that children respond well to routine. If you can establish a consistent routine as soon as possible after the big move this will help your little ones begin to feel safe in their new home environment and allow them to start exploring their wider surroundings. Don't worry if it doesn't come easy at first, be persistent but kind and soon they'll be telling you what comes next.
I'm sure my patients get bored of me telling them to anticipate difficult situations but it is a really wonderful resource not only for people with mental and emotional health difficulties but for everyone. Small children find it especially difficult to anticipate because their brains are still developing and functions like memory and reasoning are still a long way off. Try to think in advance what might be difficult for them and take steps to cushion the blow. For example, before the first day at a new school it might be helpful to talk about what might happen, how it might feel, what you can do to make it easier, and then afterwards take time to reflect upon the experience together.
Another feature of a child's developing brain is that they have less control over their emotions. This is because the cognitive functions that allow us to dominate our emotions in adulthood (hopefully!) are still developing which is why small children are prone to emotional outbursts and temper tantrums. They may experience their feelings more as physical sensations because the thought process part isn't developed enough yet. For this reason emotions can be very confusing and in a situation in which they are dealing with big changes things can very quickly become overwhelming.
Generally children respond very well if an adult helps them to start making sense of their emotions. Start by speaking about the physical sensations which will be easier for them to identify and then start offering some possible meanings. It doesn't matter if your interpretations are wrong, what matters is starting a process of thinking and attaching meaning to the sensations and then trying to put it into words with a trusted confidant. For example you might say something like "Are you OK? I'm concerned that you're worried about something. Sometimes when we're worried about something it feels a bit like when you're going down some stairs and you miss a step. Is that how it feels or is it different?".
Finally, as a mother I often see articles like this and then beat myself up about how I'm doing everything wrong! Relax! These are just ideas that can help! If you love them and make sure they know it then you're doing absolutely fine.