Sorry to move has been unsetting for you. It sh$t sometimes isn't it.
Once again I can see the similarities with my H - he insists on being friends, but only on his terms.
As for the meal, do you think you can handle it and remain cheerful, happy and calm? If not (don't think I could) perhaps you could be honest and tell him that you're unhappy with him involving OW in your family, it makes it awkward for the kids and the in-laws. How about suggesting that you don't go on tuesday, but reschedule the family meal for when it can be just the four of you. Gives you a chance to regroup your emotions.
The kids should be clear that they would be going out with OW and their grandparents and be able to make their own minds up whether they want to attend. Try not to influence them one way or the other. If you knock the OW to them it could turn against you at some time in the future. That is of course if you H and OW have a future (doubtful).