It might be that the horse is already out of the barn so it's a little late to do certain things, but...
Seems to me that the items you listed may be things that it would have been better not to allow them to be "things" to begin with. Does that make sense?
For example: movies in bed. Why was that even an option to start with? That never happened in our home. Ever. Bedtime is bedtime, beds are for sleeping (and cuddling reading a bedtime story just before lights out). Not for movie watching. Seems like a tantrum could have been avoided from the get go by simply never letting watching movies in bed be a "thing".
Same with a tablet, although I realize that my kids are older and when they were 6, kids didn't have tablets b/c they didn't exist. Lots of people allow it, but really... it seems to me like it should be more of an extra, a "special" thing, not a thing to be taken away that they normally have access to all the time.
As for losing the chance to play outside, I'd frankly pick something else to take away. You punish yourself by not allowing your kid to burn off energy. Outside is a fantastic way to do this. Kids don't get enough outside time these days as it is.
I'd cry and throw a fit, too, if I couldn't go outside, couldn't use my tablet AND couldn't watch TV/movie. Especially if I had learned that these were acceptable ways to relax/calm down before bed.
Maybe you should find different short term things to take away. Long term doesn't usually work very well until the kids are older. (teens losing a phone for example, or use of the car).
What about something else? What other "currency" does he have? Is there an outside toy that is favorite? The slide, the swing? Maybe make THAT ONE item off limits for this evening's play, but still allow time outside.
A particular movie kiddo wanted to watch? Disallow THAT movie, (since movies in bed are normally ok?) and only allow kiddo to pick from 2 that YOU select yourself. If he doesn't like the choices, too bad. He lost his choices by whatever the behavior was.
Basically, it sounds to me like you need to take another look at what you are using as your punishment/loss of privileges with this kid. Make it specific and reconsider if kiddo has too wide of boundaries to start with.
Have kiddo earn screen time by GOOD behavior maybe. Rather than taking away a device (that he has learned is his), change the rules about his usage... he now has to earn time on it. When time's up... that's it. Maybe allow him X amount of time per day, and for each infraction, he loses 10 minutes of that time or something. Also allow ways for him to earn EXTRA time. Keep a tally sheet where he can see it. It's more specific than just taking the device away. Once it's gone, then what? You lose all your leverage and your kids loses any incentive to do better.
Don't just pick your battles, strategize them.
Good luck.
Oh.. and since I seem to have done what you wanted to avoid.. sorry about that. But grounding? For a 6 year old doesn't seem like an effective idea to me. I didn't start using grounding until the kids were old enough to have enough independence for grounding to mean anything. If they aren't going places without you already, then what's the point of grounding?
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Ok, I'm really trying to understand this. You said he doesn't watch movies "to go to bed". But you also said, "They are allowed to pick something to watch or do quietly before bed..." So, he picked watching a movie in bed. Right? You said "no." Why? That seems like a legitimate choice based upon what you have told us. Was that something you took away as punishment for that night?
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After your recent SWH info:
So most of his issue/tantrum throwing has to do with coming inside after playing outside with friends? Is that what the main thing is or am I misunderstanding?
If that's the case, I'd take a look at maybe HOW the playtime ends. How long does he get, or is it relative to whatever else is going on? I mean.. does he get 45 minutes, or is it however long until dinner is ready or you're tired of checking or until they start bickering over some imagined sleight in the yard... or what is the determining factor in when he has to come inside?
Because it might simply be a transition issue. Whether you are playing in the front yard or at the park or at a play place... kids need a warning that time is almost over so they can mentally adjust to the idea of being done and moving on. While at 6, they should be quite a bit better at the transitioning than a 3 or 4 year old would be, they also are old enough to have developed rather complicated play schemes with their friends. And if they are "in the middle" of something, and he doesn't get enough warning to wrap up the game, it could be very upsetting.
Say they are playing tag and everyone has had a turn being "it" except him. It's about to be his turn, but you call to him "Billy, you have to come inside now." gasp! He won't get his turn! That's not fair! Upset ensues.
Perhaps you already are, but if not, be sure to allow adequate time to transition out of the activity. When you think you are getting ready to call him in, 5-10 minutes before, call out to all the kids and alert them that "Billy has to come in in a few minutes, so you guys need to wrap up whatever you are playing." Then maybe 2 or 3 minutes before he HAS to come in, give another time warning: "2 minutes until you have to come inside and everybody has to go home. Just letting you guys know!"
Then... step back out, "It's time to come in now. Glad you guys came to play. See you next time." Then turn and come in, and allow Billy 45 seconds to sadly tell his friends goodbye for the day. Or stand and wait at the door while he does this.
Maybe that will help with this particular issue. Giving "warnings" about something that has to happen soon, is not the same thing as giving warnings to STOP an activity that shouldn't be happening. It's just information. And alert to what is coming. Not something that precipitates punishment. This sort of thing cannot be what the counselor is referring to when you were told to take immediate action. There is no infraction at this point... you are preventing one, by giving time for a transition to happen and kiddo to adjust mentally to it.
Or at least, that is how is normally works. :)
Hope this helps.