RD - I'd see if the Hoh/d/Deaf children's support services in your area has some people who can sit with you one on one (or as a family WITH the hoh/Deaf child present) and give you some techniques on how to teach literacy skills, read to etc to your child in a way that not only teaches reading and English but also ensure comprehension.
One way that I've seen taught as a means of teaching reading at a number of mini-clinics I've attended on the topic that really makes sense, and works is:
Make sure that the child can see the signers hands AND the written text on each page at the SAME time. This requires sitting slightly differently than hearing parents read to their hearing children - with small children using pillows is helpful either to prop up the child - or the book
Make sure that you always connect the words on each page with the signs AND any pictures. This allows the child to connect the Words with the Signs as well as with any corresponding images... this forms a better connection for visual learners (ie they may see the word "Apple" and then in their mind "overlap" a picture of "an apple" so when they see one, they remember the other ... adding the sign for APPLE to this creates three connections to the single "concept" of apple
The first time through a sentence/paragraph/page (for young children's books) sign the text using as close to English Order as possible ... add fingerspelling or borrow SEE signs to show parts of speech such as - a, the, as, it, etc as well as word endings - ing, ed, est, etc . Be aware that the child is likely NOT going to understand exactly what is being said during THIS FIRST read....
Then once the sentence(s)/paragraph have been read in "in ASL English" (my phrase) using SEE or finger spelling to clarify English grammar concepts - THEN start discussing in ASL what is happening on the page (related to the sentence). Have the child as involved in "helping explain the sentence" as possible.
Once the sentence/paragraph has been signed "in ASL English" then discussed - then resign the sentence/paragraph again using ASL - this way the child truly understands in a number of ways what the sentence/paragraph says.
Once this has been done - consider signing the sentence/paragraph again in the "ASL English" ... and if possible ask you child to HELP sign along with you (or point to the English words while you sign each one. This allows them to connect the sentence they "know" (from ASL, and discussion) with the ENGLISH version of the sentence that is being signed in "ASL English"
Although I don't know anyone who uses SEE for their everyday communication (even if they learned it 15+years ago in school) I do know a number of Hoh/Deaf parents who use it specifically to teach their children how to read. They keep all the ASL signs for objects etc (instead of using the SEE) however use English word order, initialize signs as needed/preferred, and use the SEE word endings etc to ensure that when reading the various grammar rules of English are able to be seen and taught to the children. ASL is used to clarify meanings, discuss what might be going on visually on the page etc - however when reading the actual story "ASL English" (my term) is used. If the child wants to use "ASL English" to describe or elaborate on what is happening in the story then that's great as well... it demonstrates that the child is learning the rules of English
This certainly isn't the "only way", however having learned and used this system at these mini reading clinics I can say that it really really makes sense and seem to me to be one of the best ways to teach English, ensure comprehension and engage with the child when reading ... because you're telling the story to the child, talking about the story and then re-telling the story together
I hope that might be useful
(thank you, Anij!)
