The sounds 't' and 'k' are phonetically quite similar in that they belong to the same 'natural phonological class', namely the class of   'plosives', or 'stops', sounds that are short, and have the characteristic that they release a sudden, and immediate puff of air. So in that sense, it's not all that strange that the 't' has changed into 'k' in some of your relatives' names. It would have been much more peculiar (and I wouldn't expect that) if
the 't' had changed into 's', or 'f', or 'v', or 'z', for example.
These latter sounds are all 'fricatives', sounds that you can continue for a long time (until you run out of breath).
Interestingly, children often exchange 't' and 'k' in their early speech (and not 't' and 'z', for example). This has often been explained the way I do above. So the change in the name Turteltaub might have actually been initiated by children (such as many sound changes in languages historically have been accounted for).
Hope this helps to satisfy your curiosity a little bit.  Unfortunately, I'm not a phonetician, nor a historical linguist, but you could contact my friend Caroline Henton, who is a phonetician.