Try making a schedule and stick to it. You can write this, or you can make cards and Velcro them and reset each day in different orders etc.
Add in meal times, get dressed bath time etc bed time etc.
You can add in tv time, terrace time and lots of play by yourself bits- 5 minutes to begin with and then build up when they are comfortable with it. Always followed with a play with adult part - say 10/15 minutes to begin with, with the aim of eventually reducing this time and increasing the play alone time. Set a timer or preferably buy some different time egg timers so they can visually see how much time is left. If they whine refer to the timer in a neutral voice. Do not let irritation creep into your voice. Just be boring and matter of fact. Don’t engage, just grey rock so they get no reaction and it’s pointless to keep pestering you. When it’s play with adult time, then fake it till you make it. Give them 100% attention and be bright, breezy and enthusiastic.
At first this will be hard work but if you make the effort you can tweak it until they are playing alone or watching tv etc more. Don’t increase/ decrease times until they are really comfortable with it. You are looking to the long term and the pain of doing this now, will really pay off.
(You already know that giving in for a quick solution doesn’t work. The kids have learnt that pestering means you’ll give in but then it’s constant. Dh needs to understand this too)
You also need to stop the sweets completely or add them once into the schedule- or you could add a token in after the play by yourself sections that they can have if they’ve played nicely by themselves. Once they’ve collected, say three tokens, then they can swap them and be rewarded with a small amount of sweets. Please don’t let dh undermine this by giving them at other times.
This type of schedule system is used for autistic children but will be ideal for your kids op because they currently have no boundaries. The schedule lets them know exactly what the expectations are, and gives them a sense of knowing what will happen and when.
When it’s snack/meal time. Offer plain pasta and a variety of pre cut up fruit, veg and other picky bits. Food has become a battle ground and the kids have learnt that refusing gets a rise and emotion out of you. Just offer it all again in a neutral tone. It doesn’t matter if they only eat the pasta. Take it away, put what is salvageable back in the fridge and offer it again at the next scheduled snack/meal. Always make sure the pasta is available. Over time if it’s no longer a battle they might try other stuff. Don’t praise or comment. Just treat it as if what they do/don’t eat is no big deal.
Good luck.