I was tandem nursing until a few days ago, so I'll share what (sorta) worked for us. My children are exactly 3 years apart (9 months and almost 4). I gave up nursing them together within the first few months because the baby is too distractible. I also had to place limits on DD1 in order to save my sanity (she was nursing more than the baby). Initially I tried just limiting the number of times DD1 nursed to "less often," but that led to lots of arguments and tantrums. So finally I limited her to once in the morning when she woke up and before bed. After several months of this I dropped the morning nursing session. When she was still nursing 2x per day only one of the sessions would be "long" (15-20 minutes) and the other one would often be very brief. Frequently I could talk her into cutting the morning session short by offering her something better (food, a story, getting ready for a fun outing).
I'll admit that after the first few months of tandem nursing I totally lost my commitment to child led weaning, so there was a lot of talk about "one day you'll be too big for mommy milk" and time spent reading Maggie's Weaning. Reducing the number of times she nursed made tandem nursing easier, but it also probably resulted in her weaning earlier than she would have liked. Once the frequency decreased her latch got progressively worse until she couldn't figure out how to cause a letdown. Consistency and firm limits (with exceptions for illness/injury/etc.) DID seem to help her adjust emotionally to sharing her nursing relationship with her sister. I think DD1 was on her way to weaning prior to the arrival of DD2 since her obsession with nursing more often coincided with a "baby" phase that has been going on for 9 months now. I don't know if this would work for you, but DD1 is actually perfectly happy if I hold her and pretend to nurse (in the same way that she calls her underwear "diapers").
One other thing my husband pointed out is that it isn't unusual for a 3 year old with a new sibling to need reassurance and/or for 3 year olds in general to test limits/boundaries. He claimed that if she weren't still nursing we'd be dealing with a different behavioral issue. Adventures in Tandem Nursing has a section that mentions something similar where she lists normal reactions to a new baby and how they might look in a child who is tandem nursing.
Ok, I realize that probably isn't super helpful, but it's the best I've got :) Hang in there, tandem nursing is a challenge!