If a woman conceives twins with one partner what is the likelihood of her conceiving twins another set of twins with a different partner?

There are various variables. Sometimes when a woman is in their 40's two eggs can be released at the same time. Some woman has the condition known as hyper-ovulation. Women with this condition tend to produce more than one egg in a cycle. This can be genetic on the maternal side. The result of these circumstances is fraternal twins since two eggs are fertilized.
In identical twins the embryo splits and two babies have the same DNA. This tends to happen randomly. At this time there is no indication that the cause is genetic.