Since you've done the pre-reading practice of learning the sounds the letters make and have done the pre-reading blending using the word family cards, you are on the right track! And not to worry about falling behind. She has plenty of time before fall and I'm sure will catch up.
Sometimes, children are so close that it just takes a tiny shift in approach to turn on the light of understanding. You are wise to go back to the letters and sounds again, for she must understand how to blend before she can progress.
Here is a good approach to help her blend, and something slightly different from the word family cards for variety. Using the Name Game in the first story only, print by hand a list of words from that particular word family, involving your daughter in the process.
First, print across the top of the page the letters at, an, and ad as column headings. Sound these out with your daughter. Next, print the letter b, and have your daughter make the sound of b. Then add at, to create the word 'bat' in the column headed by the at sound. Have her sound the word out, covering the at part of the word at first, then uncovering it as she sounds out the word. Praise abundantly. Continue on with all the at words, then do the same with the an and ad columns. Keep sessions short--about fifteen minutes. If you haven't finished the exercise at that point, just pick up the next day where you left off.
The next session, do exactly the same thing on a new sheet of paper. You may even invite her to draw a picture beside some of the words. [cat, hat, rat]
At the third session, if she has been successful at sounding out some of the words and is gaining confidence, write the words fat cat next to each other. Have her sound these words out, and then humorously discuss what a fat cat might look like. Have her draw a fat cat next to the two words, and then return to the rest of the list. Continue in this manner until she can sound out these words, but do not return to the stories in LSLF yet.
When she is fairly proficient at sounding out these word families from the first story, introduce the word families from the second story in LSLF in the same way.
At that point, she should be ready to return to the first story in LSLF. May our good Jesus bless and guide all your homeschooling days.