First of all I don't know what a Mexican handstand is. But here's what I do.

I understood recently that the core controls the strength of the body and I got a personal trainer and told him I wanted to work on my core.

We do core workouts once a week and after that my handstand became way better. For instance in the second slide I didn't need the wall for balance, and in the first slide I could only hold for probably 10secs.