I would suggest that your eldest, like all 3 year olds, is behaving incredibly selfishly. It's what being a "threenager" is all about. This and the Terrible Twos is when children need to bring to learn that their needs are not the centre of the whole world. Most toddlers find this hard to learn, it's the reason for toddler tantrums - when toddler does not get exactly what they want when they want it.
Especially so now he has a sibling, he needs to understand (in a kind, gentle way of course) that his needs are not more important than baby's. He may well be jealous of the attention taken away from him by the baby, and this is a reaction to expressing that.
So start with positive and appropriate attention. Ensure he gets lots of positive attention and some 121 time with you during the daytime. Other practice in the daytime would be patience (wait for your attention while you finish feeding baby, for example), sharing and turn-taking and being able to concentrate on something on his own. All with lots of praise.
Then boundaries. Again, you need these set in the day if you expect to be able to set expectations at night.
If you are breastfeeding an 8 week old, why are you sleeping in the toddlers room? Are the baby's needs less important than your toddlers needs? It would certainly be true that a breastfeeding newborn needs mum far more than a 3yo who is far less dependant.
I mention this because, quite frankly, your 3yo needs to accept that his behaviour at night is unwarranted and unwelcome. Like any other unwelcome (or "bad") behaviours, he needs boundaries and expectations around it.
It is reasonable to say he will be sleeping in his bed on his own. So a process of rapid return will help him learn that. He is using the "it's an emergency" line completely inappropriately (I assume it's not an emergency?) Because because it gets your attention. That's not a need, it's the manipulation of a typical self-centred toddler. I dont mean your child, personally, is self-centred. Just that this is typical of the toddler tantrum years and a normal behaviour phase at this age.
So there is no harm, and it will do your child good, to start establishing that some behaviour is not acceptable and will not be tolerated. Destroying everyones sleep for no real reason is exactly such behaviour.
So lots of positive attention in the day. Then at night, strict face on and no nonsense accepted. In bed, kiss, leave, close door. Repeat, Repeat, Repeat, repeat. It may be a million times the first night. Be consistant and it will reduce night on night. Then in a week when he's sleeping better, you and DH are sleeping better and so is baby - then everyone will be in a better place.