Sorry to hear this ExpatAgain, I've been in your position (on an African posting) too. You said you were originally going just for 5 months, but now are you staying indefinitely? Or do you have an end date in sight - if so, how much longer to you have left there? In my mind that is key to mental stability and planning your time there (or not) to the best advantage.
If it's indefinite, it's not a bad idea for you and the children to head back to the UK (if you have somewhere to go) for a holiday, take stock, take advice from family and friends who know you best. Re-energise, research, consider. You said you have 'thinking time' there, but sometimes you can only think about your situation clearly once you're removed from it (hence we often make life decisions whilst on holiday).
Do you do anything just for you, that's not related to keeping the family and home running? A yoga or tennis class, even language lessons (whether the national language or a European one) at home. Having allies (who turn into friends) on hardship posts is key to happiness, but I also know how cliquey some expat groups can seem. Be honest with the people you meet, about how happy you are - they've probably felt the same at some point.
And finally, make it a matter of importance to spend time talking with your DH. Dinner out if you know/can find/trust a babysitter, if not, dinner at home after the children are in bed. Has he taken any time off to be in your new home yet? He may be saving up holiday for trips abroad, but get him to use a day or two just to be at home and experience your daily routine: being around the house, shops, school run etc. I think it's key for him to really understand how your life is right now and why you are unhappy.
And if you've gone there mainly for financial benefits, don't hold back on spending those benefits to get some pleasure now! Hire local staff who you like/come recommended; they can often become friends and help with childcare to boot. Hire a driver if the roads are dangerous. Buy a better car if it stretches to that, pay for sports/culture classes that look expensive compared to the cost of living, but may just be what you need for some 'me time'.
Offer to pay for the flight for a family member or friend to come out and see you, preferably asap - you need an ally!
And even if you think heading back to the UK for a holiday right now isn't right for you, book your next trip, so you have a date on the horizon to look forward to.