If you know all this then why can't you just make a decision yourself? If law gets you more money and it's a very wanted job in your country then do it.
Because I like to know other people's opinions, there are many many stuff about computes science and law that I don't know anything about, and a simple sentence could lead me either way, I don't want to go into one major thinking it would've been better to go to the other.
Try taking on some difficult tasks in both fields and see which one you like more.
Major will be the field where you don't get tired of trying to solve.
Honestly, you really want to do what you enjoy. If you enjoy your job, that's all that matters. Loving what you're doing completely outweighs your income and location. So if you really like software engineering, go with that.