Oh babes what a nightmare. I've only got 2, aged 7 and 4, and I'd struggle big time on my own 5 1/2 days a week - crikey - I can only imagine 3 all under 3!
Do you have family/friends who can support you and help out over the 6 month period? I'm lucky my mum and dad live only 10mins away and mum's retired now, so they great at helping out when needed, but I know not everyone is in that position.
Do any of your wee ones go to nursery? It might be to keep your sanity and give yourself a bit of "me time" to maybe see if you can get them in somewhere a couple of sessions a week or see if a family member could help out to let you go and get your food shop etc during the week?
When's your hubby due to go, any idea yet? It does seem totally unfair that they've chosen your hubby when, as you say, there are others in the company with no family ties, however, it could be that he's the best man for the job which is a nice slap on the back and the extra cash is always welcome!
I'm sure once you get your head around the prospect of him being away for most of the week for 6 months and plan for it, you will feel a little bit better about it...chin up honey and just think when you lose all your weight and reach goal he can spend his extra cash on buying you lots of lovely new clothes! Take care xx