Don't take them to offlead parks. You're asking for trouble by doing that.
A lot of dogs do not appreciate the rough style of play that corgis enjoy and it sounds like your two are pretty full on so would be even more annoying for other dogs.
I'd work on taking them out separately and doing training with them. Just cover the basics (sit, stay, come, down) initially, so they learn to focus on you while they are distracted by the sights and smells. Then work on some loose leash walking. You need to refocus them on you and put their minds to work so they calm down.
If you have no success with this then you should contact a behaviourist/trainer before it escalates. I can ask around for recommendations if you ever need them.
I agree with the no off lead parks. Even if yours are perfectly behaved I am not that trusting of other dogs. As for the rough play, my two can look and sound like they are going to kill each other. Teeth, snarls the whole deal, but they are playing. Sometimes I just get tired of it and put them in time out to cool off, and by time out I mean confined to their carriers. Good luck! ^..^