I think its a fair enough statement though, I'm not meaning to bag you, but whatever the situation, trying to maintain a decent relationship with kids with so little time isn't going to be easy.
It must be a fantastic job to want to risk your relationship with your children for it, especially if you know this chick to be a fruit loop (who the hell tells children that their father is dead???). You need to be able to extend your connection with these kids even further so not only do they know that (sick) information is not true, but so they have a sense of normality for at least some of the time.
At the very worst you might have to change your jobs around (hey, I dunno the real circumstances) - and for that you could change so much for these children, you could be the refuge from the crap they must have to deal with on a daily basis. You could be there for them, by just being there.

As much as I hate saying this - I have to give credit to my exH. His wife was a feckin fruit loop, would shack up with anyone, move interstate at the drop of a hat yadda yadda yadda . ExH would travel as far, he would do what he had to, to maintain the consistency with is son, he never wanted him to think that her life was NORMAL and that's what he had to look forward to. I know how precious that time was to SDS, he could relax, he could be himself and as soon as he could - he ran straight to his dads to live for good....and they all lived happily ever after.

I understand I've probably offended the crap out of you, but I don't mean to. You don't have to respond to this, I'm not demanding answers. Just giving you a different perspective.

xoxoxoxo