Oh bless you this all sounds so familiar as I was going through it just a few weeks ago but if this reassures you at all - it all feels like a distant memory now because things have changed so much since!
I have a 3 year old (and an 8 year old), baby is 8 weeks, and things are sooooo much easier now than they were at the 2-3 week stage. PLEASE remember that babies do a massive growth spurt at this point and basically want to cluster feed and co-sleep non stop, the moses basket is a complete no-no, all they want is you. Add in to that mix a preschooler who's adapting to a new baby, and only want you as well, and it's bloody frigging tough!
My little DS3 was doing just as you describe at 2 weeks, but at 8 weeks he sleeps happily in the basket between feeds at night, is going longer between day and night feeds and (just in the last week or two) has started to sit happily in the bouncy chair, or lie under babygym, for short periods during the day (previously he just screamed and screamed unless in my arms) which gives me a chance to spend time with DS2. He will also sleep for short spells in his basket during the day which again, just wasn't happening even three weeks ago!
it gets better. It really, really does. But in terms of how to cope until things calm down...others have already given you great advice...I would agree to use TV, food, stories, whatever will keep your DD happy whilst you feed. Try to do certain tasks without unlatching the baby if possible! (I can now pour drinks/find Lego/help DS do various things mid-breastfeed and DS3 just clings on and gets on with his feed
). Give lots of positive reinforcement to DD as others have said... I find a good approach is to talk to my 3 year old - and the 8 year old, for that matter - 'through' the baby if that makes sense - i.e. "look, DS3, isn't DS2 clever going to the toilet on his own/eating his sandwich so nicely/playing with his Lego? You'll be able to do that one day when you're a bigger boy". Or "aren't you lucky DS3 to have such a lovely kind big brother?" and so on and so on. And sometimes it really helps to say something like 'no, DS3, you just have to wait a few minutes whilst mummy gets DS2 a drink' or similar to the baby in earshot of the 3 year old. It might sound a bit daft, but I think you almost need to be a bit over-the-top at this stage, emphasising that the needs of the preschooler are still important to you.
The other thing that I must admit has made a big difference to us is to top up DS3 with a bottle of formula at bedtime...I breastfeed for all other feeds but he has a bottle after his bath now and it's great, because (a) DH can feed him so I can do a 'proper' bedtime story with the older two and (b) it means he generally settles during the evening rather than cluster feeding for hours so I get a bit of a break too. The mix-feeding approach is not for everyone, I know, but if you find exclusive BF is becoming so draining that you feel you can't cope then it might be worth considering.
Good luck, I am sure things will settle down for you soon. And congratulations on your lovely new DS 