I do not feel that you are wrong to be hurt. You have every right to be hurt and honestly regardless of the situation feelings are feelings and everyone has a right to their own feelings. If our partner does not agree with our feelings they should still be sensitive to our feelings just for the simple fact because that is the way we feel. In any case I do agree with you and feel that he should have definitely confronted you first and it is not right at all. I also can see why you may be worried that he may not be telling you other things based on his comment of " I should have never told you". However, looking at it from his point of view because men do not always see things the way we do. He may have just been trying to be nice since the children we to be staying. Not that he is right about that, but he may have really thought that she would say no and just felt obligated to say that because he was uncomfortable about the situation. Again, this does not make it right, but men do not always take things as serious. I understand you are hurt and you should definitely tell him how you feel and what you think he did wrong and what you think he should have done. He is not right for screaming in your face especially for the kids to hear, but it was not good for you to tell him to go back to her if he wants. He truly may not want to be with her and that meant nothing to him, so when you threw that at him he took it very personal and screamed out of frustration. Now this is not healthy for both of you. You both need to sit down and communicate. Tell him how you feel, but without throwing things in his face. If you do that then you have a better chance of him reacting in a different way and actually listening. See when we attack when we are hurt the other just defends and attacks back, but when we come calm with love explaining our feelings and telling how we feel, but in a different way the other mostly always responds in the same manner, more open to listen and less to defend and attack. I would suggest trying this. Since you both had the explosion just start off by apologizing that you threw that comment at him, but you want him to know you love him and that hurt you. Let him know that you would not do that, that you have respect for your relationship and hold it on a high pedestal and would like him to do the same, so when he invited her that hurt you a lot and you hope he can understand. This is just an example of what you can say in order for him to understand better and not get into attack mode.
About you not being able to trust him with other things. I would not jump to thinking you can't trust him because of this I would base that more on his other actions. I would ask yourself has he been trustworthy in our marriage? Does he do things like this? How is his personality? If this is the first occurrence since he cut her off then I would say to have a talk with him and continue on. Let him know he can tell you everything and you will not get angry, but rather communicate with him. This way you can guarantee he will tell you everything. Men tend to hide little things that they think are little because they think their wife will overreact. A lot of couples has communication issues. It is not about agreeing with everything or being submissive it is just about the way you handle the situation and the way you show your anger and hurt. This can make the difference in men telling their wives everything or not. You can definitely feel how you are going to feel. It is not to hide that it is just about how you communicate it.
About the next concern you had. I again would judge this on how he acts in the relationship. Do you have other concerns to make you think he wants her and is leading her on or was it just this once. If it was just this once it could have very well been innocent and not that he was trying to get her back. So I would just base this on his other actions as well and not just that one incident.
I really hope this helped you and I wish you all the best, but please take it day by day. Do not worry to much. Just think positive and communicate with him. You both can grow closer and through communication you can help him see things through your eyes.