Well hello mommy B..
As a mother of a son who turned 3 in August and a 6 month old daughter, I understand exactly what you are going through. When we first brought Averie home, the transition was extremely difficult, as it should be for Jack. Going from 1 to 2 is hard for us, but getting a new sibling turns their world upside down.. Jack has in the past 6 months turned into the MOST amazing big brother and each day after Ave was about 1 month old, it just got better. I can only tell you what worked for us.
I found that giving one on one time to Jack was THE most important. During the day, I was so tired or busy with breastfeeding, Jack got the short end of the stick and would act out. I had to make a conscious effort when Averie was sleeping to do a fun project with him or something that gave him my full attention. If that wasn't enough, when my husband came home from work, I would go on a special errand with Jack while Daddy stayed home with the baby. That was great for both parents getting individual time with each child.
I also moved Jack's carseat next to Averie so he could be next to her constantly. He learned to help this way and be a part of it. He would wipe her when she drooled or puked, console her when she was crying, and entertain her. This was his big brother job and he loved it.
I also made him part of everything with her during the day. Changing her, (he would be in charge of getting her diapers or wipees), kissing her on her belly to make her smile. He would help feed her a bottle at home while cuddling all together and I let him hold her alot. He also was in charge of greeting her when she first woke up in the morning. They both LOVE this now. Noone makes Averie smile like her big brother and he takes such enjoyment in that.
The biggest part of the adjustment was just making Jack feel like he had an important role in Averie being his sister. It was very hard the first month because she didn't do anything but eat and sleep but after that, Jack learned to adapt very well.
It all takes extra effort on your part and as exhausted as you are, I know this seems like so much to ask. But it will all pay off in the long run. I think I did half of this stuff the first month home with my eyes closed. I was at my wits end too and so tired but I am a really happy mommy of 2 now and Jack is as happy as can be.. (HA! When he is not throwing one of his awful 3 year old tantrums.....)
I hope this helps and good luck to you
K.