I don't think Idirdog is being aggressive at all and can well understand her frustration.
Too many people get pets without thinking ahead, plus this dog sounds fairly young, so chances are OP already had children when she got the dog.
Dogs are sentient beings. It's about time more people realised this. They are not disposable. They have needs and feelings of their own to consider.
Of course children's safety should come first, but no-where in the OP does it state that the dog is a danger to the children. Just that OP is struggling with his energy and it doesn't seem like a great deal of thought has been put into how to stop the exuberant behavior.
OP could make changes to diet, exercise and mental stimulation, she could crate train, she could use clicker training to teach the dog to be calm in the house, maybe the children also need training on how to behave around the dog when he gets excited.
Teaching the dog commands is not the same as teaching him what is expected of him in the house. I've taught mine to sit, stay, down etc. That doesn't mean they know not to run mad loops around the house, that requires a different kind of training.
Many, many dog owners manage with this and more each year. All it takes is a bit of thought and effort. Not too much to ask is it, bearing in mind the stress rehoming will cause the dog and the lesson it will teach the children.
One of my dogs had caused me many issues. Giving him up never occurred to me. It's just not something our family do or ever have done when faced with a difficult animal. In fact if I had have given him up without exhausting every other option available to me first, then my family would have fallen out with me over it. A dog is for life. That is a very clear lesson we were taught as children.