Hey and welcome.
I am not that experienced myself, am still at the beginning of a similar relationship structure you are talking about but I think you need to bear some things in mind when going into this arrangement.
First of all: don't lump your men together. If you start this, you will have two different relationships that both need work and individual time and space to develop. Of course there is an 'overall-relationship' kind of thing, but to make this work, don't forget that each of you needs time as a real couple as well.
For the new man in the picture, Jeff, you will find many resources here that inform you about NRE (new relationship energy) and what it does to established relationships and what the pitfalls with this phenomena can be. And don't get testosterone confused with jealousy. It may be positive to have two men compete for your attention but it can be really unhealthy to add fuel to the fire.
The sleeping arrangement is up to you three. Look what you are comfortable with, it's not all the time good to not have a place where you can be yourself and for yourself. Being forced to share each evening and night with two other people could be a strain for your relationship(s). One needs time for oneself sometimes.
How much you want to share with each of them is again part of what you (all three) agree on together. Sit down and talk with them what feels comfortable and what not. Sometimes personal preferences and no-gos are fundamentally different.
That would be some major points I can think of for starters. There are many posts on this forum that deal with the questions you asked. Search a bit and read and a lot will get clearer. As for your question with the children, there has been a post here that introduced some kind of field report from a girl that grew up in a poly family. It is really interesting, maybe you find some answers there as well.
I am sure there is more advice to come. Good luck with your two families