I would suggest a couple things, take them or leave them! And they are said in love – which is hard to get across online.
Plan visits with this particular family at places that have boundaries built in (a room/home/fenced yard instead of a store). Plan places where kids can be little and play (you are talking about 4, 7, and 8 year olds, play and noise is normal and going to the store with friends is not going to be a quiet activity -they want to play with their friends). Also do less visits if you feel the need to have some space.
For the 4yo not leaving your son alone when your son was in timeout: you stand between them and redirect the 4 year old to his parent. If they won’t leave your son alone then specifically ask the other mom to take her son to a different area while your son finishes his timeout, or even better, you remove your child from the store to do his consequences in private – timeout in the car for example.
For the lost because he was hiding and not responding – what comes to mind is how would Christ have handled it? I think he would have loved on that little one in the moment, welcomed him with open arms (thinking of the prodigal son parable here). Then at a more appropriate time when everyone was calm he would have shared instruction, probably with a story. And he would have gently reminded you (a bystander, not the parent of the child) to rejoice that the one who was lost is found, not to call for punishment.
Yes, I’ve had times when I’ve thought the same thing, ‘If they would just _____ then their child wouldn’t _____.” But that is my pride talking. I think I know their child better than they do. I think I know how to parent better than they do. That is a very slippery slope of judging others that I think we humans naturally climb onto but that with practice we can recognize those thoughts and take them captive, turn them over to Christ, and walk away from them. I still fail regularly! But I’m trying.