Gaining fluency with multiplication facts becomes much easier with knowledge of the patterns that unify them.
For example, if you want to compute 7 x 8, you might reason
"8 is 2 x 2 x 2, we have 7 x 2 = 14, and 14 x 2 = 28, and 28 x 2 = 56, so 7 x 8 = 56"
or
"8 is 10 - 2, so 8 x 7 is the same as 10 7's minus 2 7's, which is 70 - 14 = 56"
If you happen to know that 7 x 7 = 49, you can reason that 7 x 8 is just 7 more than 49, which is 56.
Awareness of the patterns helps not only because it gives you lots of possible ways to do a computation, but also because it makes the material more engaging than rote memorization, so that it sticks better.
Teachers are often unable or unwilling to accommodate students with special needs. If that's the case of your daughter's teacher, it's not necessarily a serious problem: she doesn't need to learn math at school. The most knowledgable people who I know learned the vast majority of what they know outside of school.
For alternative math learning resources, you might check out some of the threads
here: some people have liked them a lot, though I don't know whether they teach multiplication facts through patterns.