It's just so hard when you have another child, too. My DD was 2 when my twins were born. I felt terrible about it because I just could not entertain her or cuddle her or have patience for her like I used to. Like she needed. She started getting closer to her daddy and going to him instead of me, and it just crushed me. I felt like I was barely holding on with sleep and breastfeeding and taking care of the twins, and on top of that, failing as a mom to my toddler. Nothing I can say will make what you're going through easier, but at least I can tell you that when the babies started getting bigger, nursing less, playing more, sleeping more consistently, I was able to reconnect with my oldest and get back what we used to have. I still do have times where I feel bad about her not getting as much attention as she should, but at least now I can
do something about that. In the beginning I just had to let her and her daddy be buddies and feel left out for awhile.
What you said about leaving the house is so true. Those first months it seemed a huge waste of time to get everyone ready and packed up, when I was just going to be nursing before and after. I vividly remember sitting on the floor of my minivan in parking lots, with diaper bags piled around me for pillows, tandem nursing and begging my DH to go get me some food before I fell over from hunger! All because he realIy wanted me to run to Target
with him, to get us out of the house together. Easy for him to say, he's not the one tandem nursing in a weird position in the car!

I hope this makes you at least feel not alone. Keep doing your best, maybe you can go on a walk at naptime, if you can get them in the stroller. That at least lets you out of the house, which does help when you're feeling down. Mine used to fall asleep by the end of the walk, and when they were getting more alert I'd take them on a walk so they could look around and be entertained. Plus then your 3 year old can use up some energy! (I guess this depends if it's snowy where you live.)