You are correct that the GPL is more restrictive than the MIT license.
You cannot include GPL code in a MIT licensed product. If you distribute a combined work that combines GPL and MIT code (except in some particular situations, e.g. 'mere aggregation'), that distribution must be compliant with the GPL.
You can include MIT licensed code in a GPL product. The whole combined work must be distributed in a way compliant with the GPL. If you have made changes to the MIT parts of the code, you would be required to publish the source for those changes if you distribute an application that contains GPL and MIT code.
If you are the copyright owner of the GPL code, you can of course choose to release that code under the MIT license instead - in that case it's your code and you can publish it under as many licenses as you want.