A couple of responses to what you wrote and what everyone else has:
-One of the reasons I want to carry, but far from the only one, is a violent and armed ex spouse
-One of the reasons concealed may be better is my children not reporting back to him on me, he has weapons too, but likes to spin everything he can. On the flip side, time and money are in very short supply for me, so taking a class for the permit would be very difficult. Have saved for a firearm, but getting babysitters and actually going shooting? Something I will have to wait and work toward. Yes I've shot before, but it's been 8 years, and while I would like to fire whatever weapon I choose before committing to it, I am going to have to settle for doing as much research as I can and practicing with snap caps in my home after the children fall asleep.
Only you know which method of carry works best for you. I've got a 2 year old son and when I'm with him I'll conceal probably 95% of the time. My attention is taken up with him so I don't personally feel I can devote enough situational awareness to OC while I'm with him. I know true verified stories of OCers being relieved of their firearm are practically non-existant but I don't want to put myself in the situation of being the true verified story. Any other person may feel quite confident in their ability to maintain situational awareness when with their kids and I don't have any argument with that, I just know what works for me. Add to that a wife who hates guns, does not want anything to do with them, does not want to see them as another reason for me covering them up. She knows they exist, knows I have them, even chases me out the house ordering me to go to the range and enjoy myself. So I can understand your feelings of wanting things kept quiet.
If you are comfortable OCing with your kids then go for it, it's your right to choose whether to OC, CC or not carry at all.