balearic....despite advances in anaesthesia and surgical techniques there are still complications ranging from minor to rather major and life threatening situations.
There are so many complications that I will confine my answer to those that may apply to your father in law as described in your post.
A "stroke" as you have suggested is by far the most likely considering the slow recovery, the limb weakness and the necessity for a tracheostomy. This may have been due to either a bleed into the brain or blockage of an artery (embolus) which supplies blood to the brain.
Other less common complications are another heart attack, bleeding into the lung, irregular heart beats, kidney failure and so on.
He is in intensive care, well looked after and will be given every chance.
P.S.....how did you get your username?