Oh, Lolly, you poor bastard!
Yup. Been through it only just over a year ago. It does get better I promise.
With us, DD1 was not very adept at breastfeeding so once we started to give her supplementary bottles I was able to participate a lot more. What happened eventually was that I did the bottles and DW did the boobs. Result: DD1 and I are very, very close.
When DD2 arrived she had a mouth on her like the Tyne Tunnel and could latch on and stay on for what seemed like most of the day. Result this time: I wasn't anywhere near as involved as I had been first time around.
Add to this the fact that DD2, far from being the relaxed laid back second child everyone had told us to expect, was fabulously loud and made up for her exemplary breastfeeding skills by being shit at sleeping. She is also the loudest child I have ever heard. When she cries, ships in the Firth of forth start to steer away from shore.
So I was tired, work was horrible (my boss decided he was jealous that I had two wee ones whilst his two DSs were just flying the coop. Seriously, he was majorly jealous. it was very weird and most unpleasant). DD1 was vastly put out by the arrival of this loud, shitting, monster and was consequently appallingly behaved unless commanding her mother's FULL attention (so I went from being number 1 parent to less-than-the-slugs-in-the -garden which was really upsetting). the new arrival refused to have anything to do with anyone other than her mother and would scream whenever I picked her up.
My poor wife was at the centre of this, getting even less sleep and having to drink about 17 gallons of water a day to compensate for the vast amount the new arrival was drinking - so when she wasn't feeding the baby she was weeing.
In short it was fucking horrible. But we powered through. We structured a routine whereby there were certain things (like bath-time) that I always did for the baby - no matter how much she kicked off. I also took her out quite a bit (as Merrylegs suggested) to give DW and DD1 some time together.
Eventually DD2 warmed to me and now we are as close as I ever was (and am again) to DD1.
There's no two ways about it: this is not a magical, lovely time. It's nasty and cruel and often upsetting. But if you decide to get through it (and what choice is there? They don't come with receipts - I checked) it'll come good in the end.