Hi! I haven't made any felted diaper covers yet, but I have plenty of experience in working with fibers in general, so I think I can offer at least a little advice

First, are you sure the second sweater was 100% wool? And it didn't say "washable" on it? There is a variety of wool called "superwash" that has been processed prior to spinning to allow it to be washed without shrinking. (To be technical, it has had the scales on the fibers kind of glued down. Picture a single fiber with thousands of tiny scales sticking out of it along it's length, all running in one direction. When it rubs against another fiber, those scales catch each other and get stuck. Heat, water and agitation accelerate that process. That is felting. Fulling is kind of the same thing, but the word is usually used by weavers to indicate a partial felting process after weaving to give a loosely woven textile it's desired body.)
Ok, if it *should* be felting and didn't, well, give it another round in a hot washing machine. Soap shouldn't matter much, it's the agitation in the presence of water that is the important thing.
If it doesn't felt any further, it should still work for you. Really, the reason for felting it is so you can machine wash it after the diaper is made without it shrinking (i.e. felting) further on you.
The waterproofing properties of wool come from two factors: the lanolin and the physical structure of the wool itself. Remember those scales I talked about? When they're not all locked together into felt, they make for lots of complex structured air space inside a yarn. They shed water (whether or not they're felted) and if the outside of the garment does get wet, the air spaces are too random and large to effectively transmit water via capillary action. (This air space is also why wool sweaters are so warm for their light weight compared to, say, cotton.) Have you ever been caught in a rain storm in a wool sweater? Even completely unfelted, you stay dry. I wear Teva sandals with wool socks all winter. As long as I'm not actually tromping through massive puddles, they do a great job of shedding water from splashes, small puddles, melt water, etc. They'll shed water from big puddles to a certain extent, but since they're not very thick and I'm putting *mumble mumble* pounds of pressure on the soles of those socks, they can become wet underneath.
I've been wondering about the waterproofing qualities of superwash, and am going to try knitting a soaker from it. I asked about it on this board a few days ago, and just this morning realized that I had the answer to my question sitting in my sock drawer. I have several pairs of (fantastically comfortable) superwash socks from Woolrich and EMS that seem to do as good a job at shedding water as regular ragg wool socks. So, even if your sweater is "washable" it should be waterproof without felting. If it's very thin, though, you might want to make a double layer along the "wet zone" along the crotch.