I realize you have a question about social security. My goal is to help you better understand your options.
Yes, it is true that your wife can draw up to 1/2 of your benefit
However if she takes that benefit at age 62, it will be more like 35% of your benefit
She would have to wait until Full Retirement Age to receive a full 50% of your benefits
And yes - she can take whatever is highest - her benefit based on your record, or her own benefit