If you can't have a day out without them starting to bicker in the car, then turn the car around and go home. Seriously, be ruthless at the beginning. Show them that their actions have consequences.
If they fight when you are baking, the consequence is that they go and do something else, and they don't get to eat any cake.
It doesn't take much of this type of thing to let them know you mean business.
At the same time, really praise the child who is doing what you want him to do, so if two are bickering and one is not, then you go home, and the two bickerers stay at home with one parent, while the non-bickerer gets to go out (to the park, or for an ice cream/feed the ducks) with the other parent. Any sign of 'crowing' (I call it the 'Nurnur ne nur ners'!), then that child stays at home as well...'Sorry, DS2, I know you didn't bicker in the car but you are now showing off, and the consequence is that you will stay at home too'.
If the fighting is to sit next to you or to grandad, then have a chart and record turns. DS3 will have to sit next to a grown up as he's too young, but the other two can take turns. If they complain, they lose a turn.
Let them know each time that this is a consequence of their behaviour. It is very important that they recognise that they are making choices here. They can choose not to bicker, and be praised and rewarded, or they can choose to bicker, and face the consequences.
They also need to know that another consequence of this is that it makes you unhappy. Tell them that Mummy wants to live in a happy house, and to see her sons getting on.
I tell mine that if I saw another boy treating one of my children like that (when they are nasty to each other), I would dislike that child for hurting my boy. When it is one of my boys I find it very hard, because I love them both so much, yet I see one of them hurting another! I ask them how they think I should react, how should I untangle my feelings here? By the time I've finished, they usually have their arms round each other, sobbing about how much they love each other. I capitalise on that, and might choose that moment to bake that cake!
Your two year old is obviously too young to fully understand all this, but I well remember my now four year old crying 'not consequences Mummy, please not a consequence' when he was only just 3. His were simple, like 'If you get down from the table, the consequence will be that your dinner goes in the bin'. Followed through a couple of times, and he stays at the table!
It will work, and you will be enjoying great days out by the summer!
(I took all 3 of mine to do the supermarket shopping tonight after school. They were delightful, and helpful. Not one boy asked for anything I wasn't going to buy anyway (so more reminding me than asking!), and we didn't get home for tea till 6. It was a needs-must trip, but I wouldn't have attempted it 6 months ago, it would have been Hell!)