(Namechanged as some of this is quite personal..)
Agree with much of the advice here. Slings were a lifesaver for me. You can also do a lot for DD1 if you chat/sing/tell stories to her while you are physically dealing with DD2, that helped me a lot when mine were that age.
Also re the anger, I do believe now that abnormal anger (i.e. where you are thinking "why am I doing this, this is not 'normal me'") can be a sign that there is something wrong post-baby (whether you call it PND or whatever). I have had some experience with that myself, also when I first had 2 DCs - used to get sudden fits of complete rage, to the point where it scared me as well as the DCs, and was worried about losing control - used to shout at them and then feel horribly guilty, like you. But then after many months I suddenly noticed that that extreme rage wasn't happening any more, and I felt much more "normal" again and was able to deal with the stressful moments with much more normal reactions. I think it was only then that I realised something had been really wrong before... If you think this might be you, then please do speak to your GP or a (different) HV, better to do something about it now if you can.
You also haven't said how much your DP is helping out? If he is around at bath/bedtime etc then he should be helping so you don't have to leave one child to cry, and he can also take charge of them both sometimes so you can get a bit of a break. You can also split up, one of you take DD2 for a long pushchair walk to get her to sleep and get some fresh air, while the other has some quality time with DD1. If he isn't helping out then I'm not surprised you are angry with him!
Finally - it honestly, really truly DOES get better. I am one year down the line now, and it's already hard to remember the worst moments. I promise you will be looking back on this in a year or so, feeling much more like you, and much happier and more confident with them both.