You train your family, like you train your dog.
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.