American Pronunciation: Written, Cotton, Button
Note: She is talking about quickly spoken American English and not clearly spoken broadcast English. There are some Americans who almost always say the T sound in these words when they talk, like her example 1. However, many, if not most, Americans always use this sound in these words just as she is teaching you.
You can practice this “glottal stop” sound with these words:
mountain, fountain, curtain, important
bitten, kitten, mitten, written, button, mutton, carton, smarten
The teacher, Lisa Mojsin, is from Los Angeles, California, USA.