Shatter resistant tea carafe/pitcher/pot

Heat-resistant glass is called for, which will be much better suited to withstand the thermal shock of boiling water than regular glass.

I'd use a Pyrex measuring cup -- which are available in one quart (4 cup) sizes, my mother owns one. (I generally just stick with two 2 cups if I need that much liquid, but that won't work for your tea steeping process.) This may require hunting through a few stores (large places dedicated to kitchen goods generally have them) or buying online. I even found a 2 quart measuring cup on Amazon, which I've never seen in a store.

You could also get a second old coffee pot, which is similarly designed to cope with hot liquid, or do the steeping in your existing old coffee pot before diluting.

Another option (though probably more expensive than Erica's suggestion) is Corningware Pyroceram. It's a glass-ceramic, so it shouldn't absorb any odors. Originally all Corningware cookware was made of this material, but now its only some of their stuff.

You can easily get these in 1.5 quart and larger sizes.

Pyroceram can actually be used on a burner or under the broiler. It's incredibly shatter resistant (supposedly, you can freeze it then hit it with a blow torch, to no ill effect), and actually pretty good even if you drop it.

Thermal shock is what is breaking your carafes. Simply stated, you're heating them up too rapidly and unevenly.

While it's true a nice heat-resistant carafe is probably your best solution, you can also try heating up your glass carafe with hot tap water before pouring in your boiling water to temper the rapid increase in temperature.

Pour in hot water to the top to get it evenly heated and let it sit for perhaps a minute, pour it out, then do your tea thing. This isn't a guarantee to prevent breakage, but gradually warming it like this will certainly reduce the likelihood.

I use this trick with my French press beakers, which are thin and love to break easily.

Here is a very readable explanation of why glass breaks under thermal shock. The example is the opposite of your hot-water-in-cold-glass, but still applies in reverse:

So in our hot-glass-in-ice-water example, the surface is trying to shrink but can't, meaning it is suddenly under tension. And the core is put into compression by resisting the shrinkage. It's not hard to figure out which section of glass wins the tug-of-war -- the surface fails first. And a crack grows out of some microscopic scratch or flaw, growing and spreading until the stress is sufficiently relieved or the glass is broken clean through.