This will be a real balancing act. It will be very helpful to have your partner's help and cooperation during this time of transition for your three-year-old. It never hurts to try other methods to help your older child to sleep if he is ready for them. Reading stories, rubbing his back, and singing softly are all good things to try before the new baby comes, and may work on occasion, especially if it's someone else besides mom who is doing them!
It's also important while you're pregnant to tell your older child stories of when he was a baby and how helpless he was, that you met his every need quickly, and that he was too small to eat anything fun like he's eating now. Let him know that the baby will only be able to drink mommy's milk and perhaps decide together on a healthy big boy drink that he will be able to enjoy while the baby nurses. Also talk with him about the baby's need to nurse first so that her tummy is sure to be full, and let your son know that he will be able to have a turn after the baby is finished. Assure him that you will have plenty of milk for him after she's finished.
There may be times when only mommy's milk will do, and you will have to think about nursing two at a time or just reassuring him that he will be able to nurse in a few minutes. If you choose to tandem nurse at night, you will need to assess which child can be most patient at that given moment. Perhaps your partner would be able to sing to or rock the baby while her brother settles back to sleep, or perhaps your toddler would be willing to listen to a quick, simple story while his sister nurses back down. Every mother and child is unique, so you will have to see what works for you. The La Leche League book Adventures in Tandem Nursing by Hilary Flower is a wonderful resource that you might enjoy.