If you are working on a hard problem and you dog comes with the leash on her mouth, you can do what the dog wants or do what you need to do. Your dog will have to wait. Non negotiable. if you negotiate and are not consistent, you are in trouble.

Your dog needs to know that she is going to go outside, but when you say so. Dogs understand it very well. If it is a rigid schedule it works much better, it is not arbitrary.

If you are working on a hard problem and your son or daughter interrupts you, it is your job to make it clear to them that they can't interrupt you unless it is important.

They need to know you will spend time with them, on a consistent basis.

People understand it very well if you are an adult capable of saying "no". Rigid schedules work much better.

I believe you are confused. You can be disciplined and love your family. Sick child? Not the end of the world, it looks like it for first time parents. Homework assistance? You are not loving your children if you do their homework for them.

Haven't millions of people -- and lots of famous productive writers, and such, done exactly that?

Or, if you expand your definition of productivity to include raising happy children then it sounds like you're extremely productive.

Counterpoint: I too fail to maintain a concentrated, productive habit for longer than ~a week. I do not have kids (yet) now, and I've also been failing at it when living alone. I was good at cutting out the distracting presence of other people, too, and it didn't help. I conclude that, at least for me, it's not about other people. There's something within me that prevents me from sticking to a habit I try to force on myself.

If you cannot maintain schedules/habits that may be related to the presence of a family

Have you had any luck with early morning productivity?