Monica,
It's sounds like your an excellent mom who wants the best for her child. However, it sounds like you're trying and pushing too hard. Most 3 and 4 year olds entering preschool do not know all their letters or how to spell their names. Let your daughter learn at her own pace. You're doing great! The ABC mat is a great idea, but don't expect her to follow your lead.
She's probably getting frustrated because the activity is too complicated for her or she's ready to move on to something else. Show her that sometimes you get frustrated also.
All types of books are great, read to her daily. I thought the wooden ABC and number puzzles were excellent. As I did them with my children, as I put a piece in I would say that's the letter "M". Eventually it "clicks". Children learn by repetition.
Remember learning and education about aren't just letters, reading and numbers. The summer is a great time to be outdoors. Take a nature walk. As your walking say things like let's climb "over" the rock, let's walk "around" the big tree, let's climb "up" the hill. Find some butterflies, then read the Hungry Hungry Caterpilliar and explain how a butterfly was once a caterpilliar. As the saying goes "take time to smell the roses". Go at her pace, let her explore a special stone or flower.
Go to the beach, collect shells, and compare and contrast "this one is small, this one is big, this one is smooth." Count them as you drop them into a bucket.
Take out a bunch of colored containers and play with water, talk about let's pour the water into the blue container, now the red one is empty and the blue one is full. Splash each other and have fun.
Put on your bathing suits. Get some foam type soap (you can also use shaving cream, but soap is much better) and a large piece of plastic (like a tablecloth from the $ store). Cover the plastic with the foam soap. Now draw letters, numbers, pictures, whatever. After you're done drawing, rinse off with lots of water.
Okay. This one may sound nuts. But my kids loved it. Color eggs. You can use food coloring, the directions are on the container. Show her what happens when you mix a little blue with the yellow.
The important thing is to have fun.