Agree with Nelly. Ignore " My husband hated it" comments. They are out of date and anecdotal. They can however hurt terribly when you have decided you will send your children so avoid these people. Talk only to people who are mobile career expats and have had to go through the process you are going through. Most people do not truly understand your situation and can even be envious of the idea that your children might receive an expensive, privileged education, albeit at the expense of family time.
That said,one of the advantages is that time together becomes more joyful when it is rationed and precious. Most teenagers get a bit restless and pull away from you when living at home all the time and life, while lovely in its way, is not the roses and sweetness of those years of middle childhood.
Try not to send them before Year 9. You might consider going earlier and living away from your husband for a year or so, meeting in the holidays (which are frequent and long). However many international schools are very sound and should do well by your children until 13. If you have a struggling child try supplementing with a bit of private tuition.
A teenager and his/her needs are so very different from younger children it is hard to make a decision early on. Skype and texting and Blackberry messenger mean you can feel far closer than you might imagine to older children.
Look at a number of schools and look early. Do lots of research as many private schools are not worth the separation, frankly. Visit several times. Talk at length to housemistresses/masters about routines and about your feelings and fears. Schools are more flexible and caring than you might realise.
Do not assume that the "big name" schools are snobbish and not for you. Go and see for yourself. In my experience, schools remain famous because they do what they do well. Do not think that because results are good they will be hothouses and too stressful for your child. The top schools know very well if they might suit your children and will advise with honesty. The lesser ones might be more concerned with bottoms on seats.
A good piece of advice I received is that it is very helpful if you can find a good school within a reasonable distance of a trusted family member or friend who will provide the odd guardianship role by attending functions you cannot make or by taking your child for a break if you cannot be there. Though actually, if you are in Europe, there will be few occasions when you cannot be there.
If you really cannot bear the idea when the time comes to sign the acceptance form, don't beat yourself up about it. At least you will have explored your options fully with your children's best interests in mind and they will be well aware of this, whatever your decision. Good luck.