I used to work for a federal agency that dealt with this stuff and went to a lot of meetings around the OMB race/ethnic directives.

Personally, given what you say, I would check yes for you and your children.  However, it's all a personal choice.  Some people who are multi-racial or -ethnic check multiple boxes, some check just one ... it's your decision.

According to Wikipedia:

The U.S. Office of Management and Budget currently defines "Hispanic or Latino" as "a person of Mexican, Puerto Rican, Cuban, South or Central American, or other Spanish culture or origin, regardless of race".

I would say you fit that definition. It doesn't have to be 100%.

Nobody knows.  It's a huge headache for demographers and epidemiologists trying to deal with data, because everybody checks the box using their own definition.  Sometimes multiple boxes, sometimes not.  The original definition is hardly relevant if people filling out forms don't use it.  And I'm a geneticist - don't even get me started on that problem.  Hispanic/latino and/or amerindian ends up being understudied and misrepresented as a result.

I know two cute little girls who are the bilingual, jewish, blond daughters of two well-off doctors.  I don't think this exactly fits the stereotypes some white people hold, but they are in fact hispanic.

Is my grand-child-to-be hispanic?  His/her other grandmother was born in the Dominican Republic and Spanish is her first language.  My son's girlfriend and her sisters was born here, but speak a mix of Spanish and English at home.  Racially, however, they are viewed as African American.  

And ofcourse, our families heritage is almost 100 percent British.