This was my hardest transition (I've got four now and 2-3 and 3-4 have been MUCH easier transitions!)
I had my first two 21 months apart and though I really like that spacing (my second set were 22 months apart), I wasn't prepared to lose my first baby. dd2 was really high needs (cried a lot and nursed ALL the time) so everyone came and took dd1 out for fun and left me with baby. On one hand that was really nice, but several times I felt like screaming, "let me have my little girl and someone take this *#&$ crying baby please!!" So I wish in retrospect I had taken a few more breathers with dd1 and left dd2 with someone else even for only a 1/2 hour or hour or so.
I also wasn't prepared for the little bit of resentment I found I had for dd2 at times for 'robbing' me of my relationship with dd1. It obviously really changed our dynamic, but the upside was how close a bond dd1 and dh developed. Now that I talk with other moms, I realize a LOT of moms feel that 'resentment' about the loss of their relationship with dc1, but at the time it just made me feel hugely guilty and terrible, yk? (it's always easier to admit to 'failings' after the fact
So that's all I'd say about going from 1-2.
*Don't feel badly about how obnoxious your older child now seems
but try to keep it in check too and cut them some slack. Pick your battles...decide what is an absolute no go and save all your "nos" for those behaviors rather than using them ALL the time. (Even with 4 kids and older ones now, they seem to instinctively save their "acting out" for when you are nursing and not in a position to physically stop them!)
*If you can take a half hour to an hour here and there to just be with your dc1 and have someone else take dc2. The reverse is also true - if you have help - it's great to experience a few moments with just one child.
*Don't feel badly if you experience some resentment toward the baby for changing your relationship with dc1. It's perfectly normal and you will get your "groove" back with them eventually
The upside is usually a better bond b/t your dc1 and dh and/or other primary caregiver.