I think that's just because as a new learner of a language, you are still thinking in your native language, not in the language you are trying to speak.
I've learned that it is easier to learn a language if you try to skip that intermediate translation process. Dutch is actually simpler than English in many ways (just as Old English is simpler than Modern English). Part of your and your daughter's confusion is perhaps because the same verb tense can be said in multiple ways in English, but in Dutch is usually only said in one way.
In English you might have "we are eating" and "we eat" that both represent now, but in Dutch it is usually just the latter. Similarly in English you might have "we will eat tomorrow", "we are going to eat tomorrow," etc, but even the Dutch use the present tense for this, "we eat tomorrow."
In fact, Dutch even skips verb conjugations entirely half the time, and just uses the infinite.
I'm pretty sure I over use 'aan het' just to get the 'ing' back.
"Wij zijn aan het eten"
As far as making the mistake, I should just know better. I got to a level that was good enough and have stagnated there. So I make lots of small mistakes, but often I'm not aware of them.
It occurs to me that the following all mean nearly the same thing in English:
We are going to eat tomorrow
We will eat tomorrow
We will be eating tomorrow
We are going to be eating tomorrow
There might be others I'm not thinking of right now.
Modern English has a lot of extra subtlety.
Dutch:
We eat tomorrow.
Not only is a future tense avoided, and an -ing tense is avoided, and a lot of filler words avoided, but also the present tense is avoided since in Dutch, the infinitive verb itself is the actual present tense about half the time (which cannot really be translated literally here)! Such simplicity doesn't really exist in English.
I find Dutch a lot like learning an elegant, dynamically-typed programming language.
The -ing stuff is just filler a lot of the time, so the Dutch wisely just don't do that most of the time.
I don't think they are the same thing. "We will" is a stronger statement in intent than "We are going." "We will elect Trump!" versus "We are going to elect Trump!" may refer to the same election, but the former would be followed by a stronger statement:
We will elect Trump! It's great!
We are going to elect Trump! I'm excited!
I don't think it's a hard and fast rule, but if people use the future tense, it's more of a personal or indefinite statement, and the present tense is more universal and definite one.
"We elect Trump tomorrow." is something that misses this. You remove the individual ability to affirm or weaken the statement. I don't know much about Dutch and English, but I'd wonder if many Dutch people fluent in English have problems with getting taken too definitely or being seen as pushy.
I think that's just because as a new learner of a language, you are still thinking in your native language, not in the language you are trying to speak.
I've learned that it is easier to learn a language if you try to skip that intermediate translation process. Dutch is actually simpler than English in many ways (just as Old English is simpler than Modern English). Part of your and your daughter's confusion is perhaps because the same verb tense can be said in multiple ways in English, but in Dutch is usually only said in one way.
In English you might have "we are eating" and "we eat" that both represent now, but in Dutch it is usually just the latter. Similarly in English you might have "we will eat tomorrow", "we are going to eat tomorrow," etc, but even the Dutch use the present tense for this, "we eat tomorrow."
In fact, Dutch even skips verb conjugations entirely half the time, and just uses the infinite.