OMG you are not the worse mother ever!!
wanting your kids to be happy, worrying about your children's wellbeing and feelings and then researching your worries??? Best Mother Ever

You sound selfless and loving to both your children's and husbands needs. I hope you are taking some time out from their needs to concentrate on doing something nice for yourself too.
Your earlier question about when to change schools?
Your youngest will just slot right in whenever. Should be the same with your eldest but it depends on her personality and the dynamics of the kids she is with, if she makes friends easily and is put with a friendly bunch, she will love it long term.
It also depends on if you have to put them on a waiting list too, in that case, the decision is not yours, so no need to worry.
I moved dd half way through year 2 ( not a choice, but a space came up) and she screamed she didn't want to move, she would miss her friends, and I worried we had made a big mistake. 1st day at new school she loved it but made a point of telling me 'but not that much that she would want to stay' . A month later she was saying how she loved her new school much better and the people were way better.
Coming in half way suited her, she likes being the centre of attention.
From about 7yo, I recall that starting new on the 1st day was a bit nerve-wracking because everyone was excited about seeing each other again, talking about holidays, etc but I slightly preferred it as I wasn't the main focus.
Starting half way through, made me the main focus but it was a much calmer environment as everyone was well established in their routines.
I can't say that one scenario is really more beneficial than the other, they are both equally experiences that will benefit your children later in life (ie overcoming anxious moments, just keep it light).
I would suggest not focusing on it too much, because there is no wrong scenario. Either scenario you are flocked with new friends the first days, everyone wanting to know about you and being sweet. It's a great feeling being so wanted 
I wouldn't share too much about the move until about a week before hand.
I'm just thinking that there is no need to leave loads of time for them to worry about it.
Im sorry to hear your dh has anxiety and depression in the past and it's great he has recognised the potential for it this time around. I promise the kids will be fine with any move. Put your worry energy in getting dh that new job and I bet in a years time you will look back at this post wondering why it was such a hard decision.
Sleep well tonight xxx