A.H.
I too am the mom of a cling-o sorus. The way I got nursing under control was to put him on a schedule, stick to my guns, and then once he accepted it I started dropping one nursing time a month in order of which ones seem least important to him. Each time I made sure to have a fun activity to distract him. When I dropped the night nursing I told him it was sleepy time, rubbed his back for a minute and then rolled over and pretended to be asleep. Initially it's gonna be hell but remember it's good for both of you in the long run.
Sounds like you might need to have a chat with your 3 year old - explain that her brother is getting older and it's time for him to have less - "booby". Maybe even see if she'll help by playing with him?
Also, I would ask the daycare provider to please squeeze in some extra hugs for your son. Maybe he could use a few more during the day but does not get them because he isn't crying.
and P.S. I think your pediatrician's response was very insensitive! Unless she's offering to help out and wash the dishes for you I'd tell her to take a hike! Contrary to recent popular opinion, attending to basic hygiene and home maintenance does not make you a bad mom.