Overlap your two pieces of batting by an inch or two and then using your rotary cutter, cut a long, shallow curvy line in both of them at the same time. Butt these two curvy lines back up together and use a long, wide zigzag stitch to put them back together. Using a curvy line instead of a straight one can prevent the two pieces from "bunching" at the seam.
You should be able to find batting wider than 45" in many different places. Fabric stores, quilt shops, and craft stores like Hobby Lobby should carry batting in different sizes from crib all the way up to king, and at my local Hobby Lobby you can buy it 92" wide (or thereabouts) and you buy it by the yard off the bolt. Look around a little and I'll bet you can find what you need. I'm not even sure I've ever seen batting that was 45" wide. Hmmm. I'll have to look next time I'm out to see what size the crib width is.