I would say that a good relationship between parent and child needs deep love. However, most attachments can actually get in the way of deep love, for we are talking about different types of love here. Attachment-type love is that "That is my child" "I will protect them." That's fine, but "I want that child to love me." "I want that child to do what I want." If we are too attached to the child then we are going to have too much interfering in the sense of how that child is supposed to live. This may be an odd way of phrasing things. Two of my friends from high school were forced to go to their father's university. Neither one of them wanted to go, they were forced. The father had a strong attachment so that son had to do what the father says. That's an attachment-type love. If it can be a non-attached love it is not going to interfere with the deep love. It's not going to be so attached thinking that "that child represents me, that child has to do everything that I want."
To understand that we are all the owners of our own Kamma is very important. One person was talking to us once about how they wanted to have children and they said, "Oh, I want to have a child because I will bring them up perfectly, they will be loving and kind and I will teach them all about Buddhism," etc., etc. We simply said, "Wait a minute, don't you understand the child has their own Kamma? It may not be that you will be able to teach them loving things. The child will be interfered with by other conditions." For example, the minute they are in school, the parent loses lots of ability to condition a child. A child comes across all sorts of odd and different things. To give them love, to give them attention, to encourage their goodness is the best thing a parent can do, but to actually control their Kammic makeup, it may not be possible at all. The child might have conditioning that is very contrary to what the parent wants to happen.
For me personally, I have three brothers and sisters. I am very different to the three of them. I am the only one in the family who is spiritual. What happened? Why didn't my brothers and sister become spiritual if I did? First of all, my parents weren't spiritual. They taught us good ethics, they weren't bad people, but not religious in that way. So, it's pretty clear that's why my brothers and sister went that way, they followed similar to my parents' life, but what happened to me? Something else was in there, I had a different Kammic make up with something deeper that ignited and fruited and I became a spiritual person even though my parents weren't. So the same thing can go the other way.
If you don't know, there is a very famous actress in America, Shirley MacLaine. Her father was a minister, and he didn't want her to see movies, didn't want her to do any of that. Her brother is also an actor. But her father was a minister and said, "No, no, don't do that!" Parents can't always control the kids. Kids have their own Kammic make up, and as much as I became very different in what I feel a positive way, other kids may not do what the parent wants even though what the parents wants them to be is positive. To love the child and to give the child as much as you can in a non-attached way, that is what Buddhism would encourage.