First of all I don't mean to offend you in any way, I just am giving my opinion. I'm a full time working mom too at one point I was even a full time working single mom... I think it is our responsibility as parents to teach our children, and reading is something we can do with and for them especially at age 6 and 7. I know kids whine, but still set aside 1 hour every night and on the weekend, 2 or more hours, you don't even have to do it all at the same time, but spend quality time teaching your child. You aren't teaching them calculus, it's reading, you know how to read.... I hate hearing my kids whine, discipline them, if that means taking TV time away, play time.. do it, they might say ugly things like they hate you, well, later in life they might really mean it when they look back on their life and realize, hey if my parents would have just spent time with me, make me read, worked with me, give me some direction but no, they were tired because they worked all day, so I'm 2 or more years behind everyone else my age... how will that really make them feel???
My son was in daycare/preschool since he was 1 year old, I thought he was learning in there too... When he started kindergarten I found out he didn't know his ABC... I bought flash cards right away and I worked with him every day until he knew all the letters (upper and lower case), we worked on the sounds, I read to him, I had him read to me, my son was not going to fail kindergarten. My son learned, not only that, he's been a straight A student in the gifted program, he's in 6th grade now. I was a single parent at the time, I had an older daughter in school too, I had a lot on my plate, but my kids are my priority... Something that helps when learning to read, is find a book they really like, and read it over and over, when you read to them, point to each word. Then after a few times, have them read to you.
I understand sometimes having someone else teach your child is a little easier because they aren't going to act up, but I would really give 100% before doing that. My daughter is notorious for asking for help, especially with math, when I go to help her I don't solve the problem the same as her teacher taught her, I do it old school, however, I do help her, and after she's done throwing her fit, she listens and understands what she's doing.
Time is all I'm suggesting, work with your child, sure you've had a hard day and you would like to just sit back maybe turn on the TV and relax... You are giving your child more than you will ever realize. I once heard a pastor say that he's been with a lot of people on their death bed and they never talk about working more, they regret not spending more time with their family and friends...
I don't mean to sound harsh, I just think as parents, we need to spend more time with our kids, especially when they are young... They grow up too fast...
I do wish you all the best!