If you can do a signature (instructions on the site) it can help people understand your family situation without you having to go back over it with each post. Keep names out of it (so you can feel free to say whatever you need to, without various teachers, neighbours etc being able to find it!).
You really sound scared and overwhelmed. But there are things you can do. People here cope with similar situations (as well as a wide range of others) all in different ways.
You've avoided the medication route - some people do. We didn't. But there are other things you can try, such as (for the ODD-type problems) reading "The Explosive Child" by Ross Greene. There is some discussion on this book in our Early Childhood forum. If nothing else, reading it might help you get some sort of feel for what the world is like from the point of view of your children.
Further assessment, maybe outside the school system, may be useful in pinpointing exactly WHY a child has dyslexia - there can be a number of different reasons depending on how the brain is functioning. There are also different non-drug techniques which have been tried (I can't comment on how successful they are - I'm not sure what studies have been done). One method which I know was developed in Australia (Sydney) by a Dr Helen Irlen involves the use of coloured glasses - the choice of colour depends on the child - to somehow 'filter out' the frequencies of light which are causing overstimulation of the brain and interfering with visual perception. That's the theory, anyway. I remember my nephew getting a pair of Irlen glasses - his had to be dark grey, his dyslexia was so bad. These seem to work best when the cause is some form of sensory integration problem.
For some kids who seem to have visual tracking problems behind their dyslexia (and to determine this for sure, you need testing to track eye movements while they track a moving object, or try to read), there is a fun exercise you can give them - have the child sit at a desk, a small ball in the LEFT hand. The child rolls the ball on the desk from left to right. They pick up the ball in the RIGHT hand then pass it back under the table to the left hand and repeat. If you have one of those trick balls which have an inner ball floating on fluid, so it doesn't roll (some of them are like an eyeball, or a globe of the world) then the ball appears to slide rather than roll. If you can, get an eyeball one - these work the best because you encourage the child to 'maintain eye contact' with the eyeball, it helps train them faster.
But remember, this only works if the problem is one of poor tracking with the eyes.
When a good reader picks up a book and reads it, their eye movements jerk in steps across the page from left to right. Each jerk is followed by a short pause, during which a number of words in sequence are read. The eyes cannot see during the movement 'jerk' but only during the stationary bits. These jerks and stationary bits are called saccades. Sometimes in dyslexia, the saccades aren't going properly from left to right but are jerking all over the page. Sometimes the pause is too brief; sometimes the number of words read during each pause is too few. This can be dealt with by training. The exercise I just suggested is one you can do at home, once you know it's the right one.
There are numerous causes for this, including simply poor training in early reading, or bad habits picked up in early pre-reading. But the most likely cause is incomplete brain dominance. One half of the brain tends to be dominant over the other half. For example - are you left or right handed? Or are you ambidextrous? Some people are genuinely ambidextrous while others simply have not settled into brain dominance.
For example - I'm fairly ambidextrous. I write with my left hand but I use scissors right-handed. I use cutting knives in my left hand but I spread butter using my right hand. Always.
Someone with incomplete dominance will feel some uncertainty over which hand to use. Sometimes they'll use left, or right, but there is that moment of dither which marks them apart from someone who is truly ambidextrous. Such a person may go on to become a true ambidexter, or they may settle on one hand. If they continue to dither, chances are they're also dyslexic, to a degree.
There are other causes, I'm only giving you what I know from my own experience. Other reasons for dyslexia are more complex and still being examined.
One very important thing you may notice - as your children are formally diagnosed as having a learning problem, there may be a point where their behaviour improves (I hope so). This happened with us and I've seen it happen with other kids who are becoming behaviour problems - when the kid is told that their learning problem is NOT THEIR FAULT they are relived, because they have just been told that they are NOT automatically bad or naughty at heart. They don't have to take the line of least resistance and be difficult because that's NOT how they're made, after all.
Your son should not be getting bullied. The school should be keeping him safe. He also needs to feel confident in himself, which isn't easy. He needs to know that there is no shame in dyslexia - some very famous and capable people have been dyslexic. Being able to spell seems to be a vanishing art, in these days of spell-check. Get him to use a computer to compose words. There are some typing tutor programs which might also help him develop his letter and word recognition, as well as tracking. If he's having a lot of trouble, enlarge the type to as big as he wants it to feel comfortable, and work from there. As his skill improves, encourage him to slowly drop the size back. Once he's composed a story or piece of writing for school, you can always change the font size back to something presentable for the teacher, before printing it out.
Once again, this is what also worked for my nephew. I don't know how he would have gone with the ball tracking exercise - that's one I invented for some coaching students of mine who were dyslexic, and the coloured glasses hadn't worked for them. My exercise did help them somewhat, but it needed more repetition (10 times a day, every day, spread through the day) and they were in their teens and not interested any more in learning to read properly.
Anyway, this is just a few ideas thrown together. I have no way of knowing how useful it is likely to be for you - I really do think your kids may need more assessment, perhaps at least initially, as a group. I also have a family full, I got the best results when I presented the whole lot and said to the doctor,
"Some things they have in common, some things they do not. I'm not an expert, I'm just a parent. Please help me find what is the common underlying cause, then we'll work on each for more individual detail."
My kids ended up supporting each other too, as they compare notes on how their brains work! No shame, just curiosity and using the knowledge gained to grab back advantages previously lost.
If medication is suggested, please at least consider it.
Good luck, Keep us posted.
Marg