Re: 4 month old - Throwing up problems!
I like the raincoat approach. I also like your doctor's approach, because honestly spit-up is only a concern when the baby isn't gaining well or isn't producing enough diaper output. In an otherwise healthy, happy baby, it's a laundry problem, not a health problem.
If you're looking for an explanation for what you're seeing, there are a lot of them. A weak stomach sphincter would be by far the most likely explanation, but it could be something you ate or it could be that your baby's pre-nap feeding was a relatively long time after her last one, which means that her tummy probably gets extra full. Or it could be that your baby is trying to nurse to sleep, and therefore takes in more milk than she's actually hungry for. Or it could be positional- if you're lying her down right after nursing, that increases the chances of spitting up.
So, what do you do about this? If this were my baby, I probably wouldn't do anything like eliminating the coffee or any other suspect food group, She's happy- to me that says that this just isn't a big problem. But I think I would try nursing in a reclined position and keeping her upright for a bit after nursing, just in case this is positional or the result of too much intake.
Coolest thing my big girl said recently: "How can you tell the world is moving when you are standing on it?"
Coolest thing my little girl sang recently: "I love dat one-two pupples!"