I agree with you completely. My father was an immigrant, as were his parents. They all learned to speak English promptly. I was taught about their culture, learned a little of the language as a child, and visited their native country, but I am a wholly American, and my parents never suggested that I was a Slovak or Slovak-American. The difference is that the Mexicans, as you note, have a contempt for this country that feeds them, while my father revered America and fought for it, so I was brought up to take pride in it.
My sympathy for illegal immigrants is extremely limited and I think it's shameful that we are permitting them into this country when there are millions of our own people out of work.
After reading your post and thinking about my mom and her friends who came from Italy, I think I finally see the deep loyalty and appreciation that these immigrants that came over 40-50 years ago had for the U.S. Probably more so than many native-born Americans.
What a change there has been with all the illegals demanding free hand-outs and then thumbing their nose at us! It is really sad to see.