I think it's important to recognize that institutional schooling represents a sort of contracting out of the academic education portion of the responsibility for raising a child, and that this is a relatively recent practice in the scope of human history. The idea of having separate roles for "teacher" and "parent" is a little artificial.
Imagine if you will that the government began providing universal free meals for children. Cafeterias would be set up in neighbourhoods and three times a day children would be delivered there to receive the meals cooked and served by trained nutritionists. These nutritionists attended special training in handling the cooking needs of large groups, and in managing the crowds of children, their table manners, their social behaviour during meals and so on. This quickly became the norm, with almost all children reporting to their nutritionists for their meals. If you as a parent decided to feed your children at home that would be allowed but considered a little unusual.
So if you decided to feed your kids at home, you would not say "It's important to be clear about my dual roles -- at certain times I'm their mom, and at certain times I need to act like their nutritionist. I need to learn how nutritionists act in order to successfully feed my kids at home."
A little silly, don't you think?
I see the distinction between "being a mom" and "being a homeschool teacher" in a similar light. They're not separate roles. We tend to see them as separate because culturally we have made an artificial separation, assigning the roles to different people. If they're not going to different people, they don't need to be different. If you stop thinking in terms of this dichotomy, I think you'll see less tension in your relationship with your homeschooled child.
Like others have suggested, there's potential conflict over the work of learning, chores, hygeine, and so on in the parent-child relationship whether or not the child goes to school. That's just the nature of raising kids: they are born immature and unknowledgeable and we have to nurture them along so that they gain maturity, wisdom and experience. Creating a warm, positive, empathic parent-child relationship has less to do with the daily issues you're grappling with than the philosophy and approach you use, and the energy and creativity you put into finding your path. The wonderful thing about homeschooling is that you have so much time and so many intimate arenas where you can use this energy -- and so few fixed requirements, mixed messages and conflicting values outside your home that can get in the way of that work.
For example, if you have a child balking at, say, timed math drill sheets and he's in school, you have to deal with the reality that those facts have to be learned based on someone else's agenda, regardless of your child's intellectual and emotional readiness. Your parenting will consist of enforcing something you don't really believe is optimal for your child and dealing with the emotional fallout of your child's frustration at school, without the power to change the expectations and requirements. If your child is balking at the same task and he's homeschooled, you have the chance to reframe the expectations, adapt the learning format, make a diversion into something else for a time, engage him creatively in a different manner, do the work at a different time of day, discuss with him how it would be more meaningful, and toss out the current approach if you think it's not serving him well. In short, a homeschooling taskmaster is empowered for creative problem-solving, whereas the parent of a schoolchild is a taskmaster with her hands at least partly tied. Almost all the homeschooling parents I know say that their relationship with their children has been strengthened because of homeschooling. There's simply much more opportunity to work the kinks out and build relationship when you are working side by side so much of the time.