I am a parent of a special needs child, also (DD12), and yes, it can be quite challenging at times. But, it can be very rewarding at times, too! I didn't start hs mine till she was 10, almost 11, so I'll just offer you some ideas of what I would maybe try if I was in your shoes. Most of all, especially since he's having some frustration issues, I would try to make a lot of his "schooling" fun. At 6, as PP said, you don't have to do a lot of formal training, but you want him to understand that learning can be fun, and doesn't always have to be hard. Not sure about the requirements where you are, but here in WV, I just have to show that my DD is making progress from one year to the next. I don't have to show that certain skills have been obtained. The 5 areas I have to show progress in are language arts, reading, math, history, and science. We do a portfolio option, rather than standardized testing, as DD doesn't test well, and may not be learning the material being tested in, due to her issues.
We, too, have lots of tears some days, but other days can be fun and smiles and laughter. I don't get a break very often, so I enjoy the times I do have. Maybe take some time for yourself and read, take a short walk, go to the grocery store (it can be quite relaxing when you're alone!), etc.
I applaud you for taking on the challenge of raising this little boy, who I'm sure has won over your hearts, even if your family didn't agree about what you've done

Stay strong and take the time to smell the flowers with your little boy. Hopefully, with your work, he can catch up developmentally, but if not, love him as he is, where he is, even on the days you just don't think you can love him (I know we have those days, sometimes) Good luck! Keep in touch here and keep us posted on his progress! Don't give up!