Lots of people will tell you it is fine, military postings are longer etc etc. And they may well be right. However, I wonder if any of those kids were ever asked as adults how it really impacted them.
I am afraid that for me it would be a hard no. My dad used to work away a lot when i was young. He wasn't military but his job took him all over the world. As a result I have very little memory of him before I was about 7 and those I do have were very negative. We don't have a great relationship and this is one of the causes.
I understand your reasoning, she is your mum, but for me I couldn't do it. My dd has never been without me for more than 5 days and then she was only a few hours away and on holiday with my parents.
There are things you need to consider if you want to go ahead, and I am not saying you shouldn't. You know your kids and how they will likely cope, but as I say I couldn't do it and I know my dd would not cope with 6 weeks without me. But consider;
What happens if 1 of the kids has an accident? How easily could you return?
What happens if their dad has an accidet or takes ill and can't look after them? Where is your back up? How easily can you return?
You say their dad, not your partner/husband...is he willing to have the kids for 6 weeks?
Where do you stand legally if he doesn't want to hand them back at the end of 6 weeks?
Unfortunately when family live so far away there are sacrifices that have to be made.
You need to do what is best for you and your kids.