This article by Althea Solter is good.
http://www.awareparenting.com/tantrums.htm
Here's another good one:
http://mothering.com/respectfully-dealing-tantrums
I think it might help to reframe this a little bit in your mind. In my mind, a tantrum is a loss of control. It's not a deliberate act of misbehavior, especially in one so young. Yes, I know your 18 month old looks big compared to the 4 month old, but really, he's still an baby.
The period between 18 and 24 months is often very very frustrating for toddlers because they have definite wants, but often not enough language to be able to articulate what they want. They also have very little control over their lives, and not enough motor skills to do a lot of the things they want. A tantrum, then, is a way of their releasing their stress.
Instead of viewing this as "acceptable" or "unacceptable" behavior, I find it useful to think of my job as teaching my child to manage their out of control emotions. At 18 months, they are going to rely on ME to do most of the work for this emotional regulation. With one of my children, that meant standing back until he was done. ANY intervention (trying to talk, touch, hug) in the middle of the tantrum made it worse. For my other child, it meant holding her and rocking with her. She needed physical touch and words to validate her feelings. "You're really angry." "I can tell you're disappointed." My son needed those words AFTER the tantrum. But labeling the emotions helped both.
Now that she's older, we're putting more of the burden on her to self-regulate. We'll offer a hug, and some comfort, but it if goes on too long, we ask her to take it to her room for a bit. At 6, she's getting better, but she's a child who feels things very deeply and it's hard for her to self regulate. She still needs to process things verbally, and so she will go on (and on) sometimes about things that bother her.
The other thing to do is to think in terms of prevention. Many tantrums are the result of overstimulation, anger hunger or feeling disconnected. The letters in HALT can help you think about this: Is my child Hungry? Angry? Lonely? Tired? If they're hungry -- a snack every 2 hours. If they're tired, make sure they get enough sleep, or engage in a calming activity. Angry? What are acceptable ways to express anger in your house? Work on those behaviors with your child.
You have a hard job because you've got an infant and a toddler, both of whom need a lot of attention. Don't worry about your 18 month old teaching your 4 month old to tantrum. (Your 4 month old will figure it out all by himself one day!) Instead, work with your 18 month old to help regulate himself. It may be cuddling, it may be standing back.
