I couldn't find any info in the mechanism at the genetic level for why Thalidomide children happened.
Did this not occur in Thalidomide children?
The deformities of the thalidomide children were the result of thalidomide's ability to block the formation of new blood vessel systems in the body. The body's ability to form blood vessel systems is vital during fetal development, because arms, legs, etc. require the development of their own individual blood vessel systems to develop properly. You can think of the stunted or, apparently, missing, in some cases, limbs of the thalidomide children as body systems which were not supplied with the necessary nourishment for their normal development.
Interestingly, thalidomide, along with other drugs which, similarly, obstruct the development of new blood vessel systems, are proving to be quite beneficial in the area of the cancer treatment. The body's capability to develop new blood vessel systems is only really needed when new body structures are being developed, and is rarely in evidence in the human body apart from fetal development, menstruation, and cancer. In order for cancers to go from being pin-prick sized groups of abberantly multiplying cells to life-threatening masses, they need to grow, and, thus, need to develop their own blood vessel systems to supply themselves with the nourishment required for growth.
If blood vessel system development is obstructed, cancers cannot grow to life-threatening size, and, thus, can be controlled. Thalidomide and similarly acting drugs are currently being tested to determine their effectiveness in fighting cancer growth in humans. The most effective dosages and schedules of treatments are currently being worked out. To date, the results are mixed.
Please don't confuse teratogenic effects, external effects which cause damage during development, with germ-line mutations.