I found going from 1 to 2 children a lot harder than I had anticipated. I found having a first child a total breeze (and was expecting it to be such a huge shock) that it made me complacent about having 2! Mine are 2 years 1 month apart, and we had also just moved areas and didn't really know anybody, no family near etc.
I went a bit nuts trying to give DD1 everything I'd given her before - we went to at least one group/class a day, did baking, did painting, and all sorts. I should have been easier on myself. It's true she and I both needed to get out every day, but the moment I gave in to the fact that TV was not evil, cake-bribery got us through the day, and potty training etc could wait until I could bear it, life got much easier.
They are now 3.5 and 18 months and I would say it has got easier and easier. I found a couple of really lovely local friends also with 2 under 2 at that time, and for a whole year now we have been taking turns to host toddler tea every Friday while we drink wine. This has HELPED - especially having people going through similar and knowing they feel the same. It is easier because my eldest, who is full of beans and chats all day long and sticks with me and wants to play all the time, has become much more tolerant about sharing me with her little sister. She has also become much better at pottering on her own, amusing herself with toys etc. This is definitely an age thing as she can play imaginative games - putting her dollies to bed, pretending to be an astronaut and going to the moon, etc - without needing input. At 2 she needed input. She also HAD to get out every day or she'd go nuts and so would I because at 2 she couldn't sustain any activities at home. Now she can - we can play games like Hungry Hippos for ages, or do crafts, and she can watch a whole DVD no trouble, or we can do a puzzle for an hour. So we can stay at home because the options are so much better.
Also DD2 was basically carried in a sling for the first 10 months of her life so I could get on with things and because she only wanted to snuggle :) , and has always been quieter, a better sleeper, a better feeder, etc, so now she is walking and beginning to communicate she'll also have spells of pottering about by herself.
I have to say I did terrible things to get sleep. I let DD2 sleep on her tummy from six weeks old because that was the only way she would sleep. I really regret that, even though of course she was fine. She co-slept in her cot (attached to our bed) for six months. We did a version of CC at six months even though I was dead against it for DD1 (different situation - DD1 is a sleep-resister, DD2 wants sleep and actually gets annoyed if you're there pissing her off with cuddles and lullabies, so it seemed the only way), and I'd rather not do that again even though she actually cried much less when we did that than when we tried to get her to sleep ourselves! But I sympathise - we needed sleep and we went to any lengths to get it. It did make a huge difference when we got it. You'll get there.
It depends a lot on their personalities, obviously, but in my experience it got easier and easier as it went along. Now I want another :D