Your doubts and restlessness are normal, and it can take a while to see that learning takes place outside the narrow view most of us have when it comes to education. So, if nothing else, take heart in that many people have been where you are and have felt what you are feeling.
Can you recall a time that you learned something new? Either as a child or adult, something you intentionally sought out or something that just happened seemingly out of nowhere? That happens for children too. People (and kids are people too, lol) learn constantly through what they see, hear, touch, taste, think, and so on. It can be tough to see the connections at first, but trust me... it's happening. There's no way for it NOT to be happening, It's how we learn to walk and talk, kwim?
Many children are not ready for reading at 7. Instead of focusing on "learning to read" you could maybe read stories, create stories verbally (I think storytelling is an art!), listen to books on tape, discuss your favorite authors and stories, tell the kids a story and have them draw the pictures if they are interested & then have them tell you a story and you illustrate instead! You can show them different languages for fun (my kids thought braille was really cool when they were little). The point really being that the reading will come, but in the meantime language and words are literally everywhere.
Breathe deeply, it takes time. :)