Obviously it does not please me that you are either unwilling or unable to enjoy time on your own with the kids, but you must live with that choice
I know you hurt, my dad cheated on my mum and left us all for her. never took us anywhere though.
My OH has a DC and his Exwife sends crappy little messages like this ALL THE TIME, tries to get her DD to send photos of me and my DC so she can see what i look like etc, totally unacceptable. I've had all manner of crap from this woman, watched her terrorise and bully her DC to the point of threats of self harm. Why? because we took her DC out to somewhere that was a good day out.
I digress.
As recent as it is, your messages won't make a jot of difference.
FWIW my ex was divorced years before I met him, the ex divorced him, but she is constantly digging at us all, telling what we watch on TV, where we should go on holiday, days out etc.
I would NEVER allow us as a couple to share a hotel room with his DC and mine.
Bottom line is that the kids feel disloyal about going on the holiday with their dad, they probably want to go, but don't at the same time.
Perhaps its too soon for them? perhaps they need your blessing to go? perhaps you need to tell them that yes you will miss them, you will feel weird etc, but it's the first time for you all to do this, so it's understandable. tell them it's a holiday for them and if they want to go they should go, that you will be excited about what they tell you when they are back.
As for contact while you are away, if it's not possible, it's not possible. Like the old days...
As for safety, their dad is in charge. they are with him. they will miss you too. it will be weird for them.
Speak to your kids to see what they would be happy with - perhaps this big adventure is a little too much too soon?