I'm seeing two concerns in your OP. One is when your child isn't like you and one is how to help a child who is struggling academically.
As far as the first, when your child isn't like you — my dd1 isn't like me or my DH. She's most like my MIL (who drives me and DH crazy at times, but is generally a like-able person). I struggled with this at times, especially when dd1 was younger, and especially after dd2 was born because I felt like MIL favored dd1 (still think she does a little) over dd2. They do have a special bond, but dd2 is such a strong person now and secure in my and DH's love and knows MIL loves her, too, that the special bond between dd1 and MIL is really a blessing and not a cause for concern.
As a kid I was pretty easy going and did well in school, loved to play outside and climb trees (tomboy), hated wearing dresses. My mom had to bribe me to wear one to school once. And then when I had dd1 I got this girly girl who wanted to wear pink and sparkles and take dance classes. It was so not me! And then there was the thing with MIL. At times I felt that dd1 preferred MIL to me! Ouch! I did resent that for awhile, but I came around on the pink and sparkles and dance class. I could just see how much dd1 enjoyed all that stuff and I found ways for her to revel in it that were acceptable to me (no knights in shining armor coming to rescue the poor helpless princess) and honored her feelings.
The reason I'm going back this far is because dealing with all this helped set me up to deal with dd1's academic challenges as well. Dd1 is very smart and has an incredible memory, but she struggles with organization and focus and anxiety. It's worst in math, but she struggled with reading for a long time. For her it was anxiety getting in the way of the reading. We wondered if something was going on with her eyes (visual tracking problems) or if she was dyslexic, but it was really all anxiety (another of MIL's traits) that was getting in the way. She would completely refuse to attempt to read all through K-2nd grade and often broke down in tears (great wracking sobs that lasted hours) over it both at home and at school. Finally in 3rd grade she began to do a little bit and then in 4th grade she picked up the Harry Potter books and now in 5th grade she's reading above grade level with excellent comprehension.
We were in private school for K-4th for dd1 (K & 1st for dd2) and we chose that because we knew dd1 could not cope with a traditional public school setting even though the public schools in our area are generally regarded as excellent (probably the best system in the state). I do think it was the right thing for her. This is her first year in public school and math in particular is really challenging for her in the public school setting. There's just not a lot of wiggle room with the teacher that she has right now and since she has anxiety issues anyway it's not a good combination. Focus continues to be challenging for her, too. She exhibits some ADD behaviors, but I really think those are a result of her anxiety. She's anxious about the problem so she can't focus. When she can focus she can usually understand the problem. We can help her focus (sometimes) at home, but at school it's a different story. It's a dangerous cycle because if she doesn't do well in math then she thinks she CAN'T do well in math which then makes her more anxious about math which makes her have a hard time focusing which makes her do poorly.
I just try to meet her where she is and go from there. That's one of the things I love about her homeroom/science/reading teacher. He meets kids where they are. Her math teacher unfortunately expects the kids to meet her where she is and that's just really hard for dd1. Dd2 does much better with that kind of teacher. She's doing really well academically and through little effort on her parents' part.
A book that I think helped me early on with some of the differences between dd1 and me and between dd1 and the rest of the world (excepting MIL) is "Kids, Parents, and Power Struggles" by Mary Sheedy Kurcinka. If you can get your hands on it, it might be helpful. I don't really like the title because it's not about Power Struggles so much as it is about becoming aware of differences in temperament between you and your child. It doesn't deal with academics specifically, but IIRC there is some mention of it in there. It's definitely not a one-size-fits-all book and that's what I liked about it so much. Kurcinka recognizes the differences and unique qualities inherent in each child and parent and offers tips to facilitate connection between parents/kids with very different styles. I used to say about my dd1 that I know all kids are unique, but some are more unique than others. This was the first (and one of the only) books that resonated with me and I felt like described my uniquer-than-most kid.
For the specific academic challenges your dd is facing there are a lot of different approaches. Is she really struggling with reading? It could be a dyslexia issue, a visual tracking issue, or any number of things. There are some specific physical tools she can use as well as teaching techniques if that's really a problem.
Sometimes, though, kids do make those leaps like my dd1 and like AllisonR did and it's a matter of keeping on plugging away and encouraging and trying not to push too hard, but push just enough and suddenly — pow — there they are zooming past that milestone.