This is a great time to start getting the daddy involved.
I have 2 little boys and when I was pregnant with baby#2, I gradually started letting/encouraging my dh to do the bedtime routine. So now, he does bath and gets teh boys ready for bed while I clean the kitchen after dinner.
I come upstairs and hug/kiss them both, and send the older boy (he's 3 1/2) to his room with his daddy where they read some books together and I snuggle up with the 20 month old and nurse him. He does many of the things your 20 month old does, lol. Eventually he gets tired, nurses a few times in between all his antics and falls asleep in our bed.
My oldest son moved to his own room at HIS CHOICE when he was about 2 3/4 - not quite 3. He knew the room was/is his and his brother's, he just didn't want to be in it til then. He's been happy and secure in it since. Every once in a while that's not true and he spends the night in our bed. It's all good.
I'm hoping that his brother will decide similarly to move. . ..
Really it's not that difficult with 2 little ones - you just have to remind the older child(ren) often that baby is delicate and needs to be treated gently and lovingly. Realize too that the first 6weeks or so may be quite memorable and sometimes difficult, but after that, it gets easier and they become the best of friends and inseparable and when the youngest is mobile, look out! they team up and man, the things they think of to do!!! . . . .at least that's been my experience.