This is a little different from your situation and doesn't directly address the nursing issue, but the underlying issue may be similar, When my DD was around 3.5, DS (around 11 mos) started walking and needed much more supervision and attention. Prior to that, I had been willing to read books with DD pretty much any time she wanted and for as long as she wanted, because DS would just happily play nearby. Once he was mobile, that just wouldn't work. I couldn't keep him safe while sitting on the couch reading all day, so I had to limit book reading to times when DS was nursing, asleep, or when DH was home to help. DD was NOT happy about this and we did see an increase in acting out/attention getting behaviors.
One thing we did was to try to have a regular time when DH could be with DS and I could spend one-on-one time with DD, even if it was just an hour a week. I think she was really missing that attention and that helped a lot. Also, we tried to acknowledge her feelings a lot, e.g., "You're feeling sad/angry/disappointed, etc. that Mommy can't read to you right now" or "It must be hard to have to wait for Mommy's attention sometimes," that kind of thing. That has also been very helpful. Also, just giving it time helped. Like everything else, it changed with time.
Hope this helps!