At the age of 5&3, it is hard for them to make a link to being good for a day out because the concept of time doesn't really make sense to a child. They live in the "now" and generally they want your attention and validation. If you work with that then they generally behave well.
Mine are 5&7. mine behave very well although they like to push the boundaries because they're quite clever and stubborn. What worked as toddlers:
- giving two choices (this didn't work once they were 5 years old!) eg sit on this chair or that chair
- giving them little tasks e.g. Make a train track in a circle, chose a colour etc
- saving the "NO" for hitting/really dangerous stuff. I introduced time outs when my oldest started hitting, keeping it very brief (clear warning, then a quick time out to say why etc), but we didn't have to use them long. I didn't use them for anything but violence
I read a couple of parenting books which helped (how to tame your toddler, positive parenting).
Basically parenting young children is hard work simply because you're always having to think and anticipate. And accept that they're children and don't always know how to behave and require teaching. Telling them the right thing instead of the wrong thing is better - how do they learn otherwise. Eg if you're learning to drive and the instructor just barks at you "don't do this, don't do that", you might learn eventually but it's better if they say "do X".
I read somewhere about using a firm voice to command your child. Again this works well. "DS, come here to mummy", "it's time to brush your teeth" etc etc. Instead of "I'd like you to come over as I'd like to brush your teeth".
With your oldest - if he's eating all the time, I would be asking myself is he actually thirsty or getting enough to eat at meals. I would also not have any cake/biscuits in the house. Sugar is addicive. My oldest loves to eat a lot, but we constantly remind him that he should not have treats all the time. Also we:
- make sure he drinks plenty of water and have done since they were babies.
- make sure that they have healthy snacks too. What works is putting out some chopped carrots&hummus/cheese/fruit before they ask and leaving them out around snack time. They'll eat them then.
- let them have sweets occasionally eg at the cinema etc.
Basically my parenting is a mis mash from reading so many books and listening/watching my child and my reactions and getting to know them and what works.
My current read is "Calm Parents, Happy kids". Brilliant book.