You say your son has learning disabilities. What does this mean specifically? Is he mildly retarded, or is it dyslexia, or does he simply get bad grades? Modern terminology leaves much to be desired in terms of clarity.
Is it possible that your husband is ashamed of his son because he does not do well? It would help if you told us why your think your husband mistreats his son.
There are little cameras that are possible to disguise -- they are sold for people who want to know what the nanny does when they are not around. I think one of them even comes disguised in a stuffed animal. You could put one of those up, in an unobtrusive spot, and if your husband catches you, you could tell him that you need to know what your son does when he is alone. But you could really be watching to hear the tone of the conversation and see the interaction between husband and son. At least that way, you wouldn't have to be dealing with a cloud of "I'm not sure."
If a mom has a gut feeling about something she is usually right, my gut feeling tells me you need to protect your son, I believe him.
There are a lot of wrinkles to this story.
First, it's natural for fathers (or mothers) to favor children who are more pleasant to be around. It's just a human reaction to a child who is difficult to be with vs. one who is easy.
I don't think a 9 year old and a 4 year old should be punished the same for the same thing, because they are worlds apart. But I do think if she's STARTING things, she should be dealt with separately because it sounds like she's realized it's fun to get her brother in trouble. That needs to stop.
I think family therapy would be great for your whole family, to work out these dynamics. I don't think this is beyond hope - at all - and your husband does seem open to changing.
One final note, it struck me as very unusual, and I had to reread this section, where you seem more comfortable with your son being loud and defiant, than the way he is around your husband, a more pleasant cooperative child. You state that loud and defiant is his natural personality and it's squelched when your husband is around. That dynamic - that you accept that being inappropriate and defiant is your son's natural personality and are upset that he doesn't behave poorly in your husband's presence - is a whole therapy series right there.
I am sorry for the confusion. I only meant to state that when my husband is not home he acts normally for his condition of ADHD, Anxiety, and Disruptive Behavior Disorder. I do not tolerate the misbehavior when I am the only one home. He gets appropriate punishment for being defiant. I just meant to state that about 6 months ago my son acted the same way whether my husband was home or not. Now my son crys when I have to leave him with his father and begs me not to go. When it never used to be that way.
Also on my daughter. I was only stating that she never gets any punishment what so ever unless I say something. My children dont get the same punishment for disobedience because they are of age difference. But the only time she gets punishment at all is when I say something.
Concerned, it really sounds like there is a dynamic in your house that you've got two teams - you and your son vs. your husband and your daughter. A good family therapist could sort this all out and put you and your husband back on the same team -