Embroidery Floss into baby bibs.

Can you get a larger-eyed needle, like a carpet needle?

These are very handy:
You can buy them in any fabric store. But a lot of embroidery thread is three or four stranded, so you can make it smaller, finer and easier to fit through the eye of the needle if you only use one or two strands - just unravel it.

I always wrap my thread around the needle and pull and then find it easier to get the thread in the eye of the needle than if I just try to stick the end through.

You don't want to use a bigger needle, especially in something as delicate as a baby's bib (unless it's one of those terrycloth bibs) because you'll be able to see the needle holes.

my wife also untwists or unravels the larger threads

Mompad knows how to embroider. Most embroidery is done with three strands, the thread typically comes twined with six. You just divide the twist into 2 three strand sections and give a little tug to get them apart. You still might need a different needle. Ask at your craft store for embroidery needles and they will show you the proper type.