I cant imagine how hard this must be for you, especially keeping your children as first priority. can I ask why there would be more problems if you were to tell you dad and brother?
Also, there are resources that you can reach out to that can give you a safety plan if you ever decide to leave. have you ever reported any of this?

Ok, I may come back and add more after some sleep, but there is one part that I just had to respond to before bed. You are a grown woman, he did not "spank" you, he physically ABUSED you. I get it that some couples are into that in the bedroom, and as long as it's consensual, hey whatever floats their boat. But you said he was "set off" by the arguing and then told you to bend over and then struck you. I'm pretty sure that no matter where you reside, this is no less than assault and/or domestic violence. It's not a short jump from you being the recipient, to your young children. Everyone always says "Call 911, and press charges" but those of us who have lived it, know it's not quite that simple nor effective in the long-term. I never told my dad or my brother about anything, either, until several years had passed since the divorce, for pretty much the same reason as you, I didn't want either of them to end up in jail, and given their reaction a few years later when I did tell them, I was certain that I'd made the right choice. But as hard as it is to convince yourself, you have NOTHING to feel ashamed of. I am in the process of divorcing my 3rd husband (widowed by the 2nd), and up until recently I blamed myself for "not seeing what everyone else saw." He was never physical, but I did see the signs pointing that way, and chose to end it. I did call the local women's shelter in the next day or so, and they offered to immediately come and get me & my kids (as far as I'm aware, all reputable shelters offer the same thing, day or night) and I declined, but I did get their assistance in actually filing the divorce, and later on, filing a restraining order.
I have no idea if you are able to browse the Internet or even make a phone call without him asking questions or being nosy, so I will leave the toll-free number to the National Hotline for you here: 800-799-7233 (799-SAFE, if that's easier to remember). After I got away from my 1st husband, someone gave me that number, and I've kept it saved in my phone ever since, but always under a random name like some business I used a lot, etc. You may never need it, and I pray you never do, but it's there 24/7 if you do.
I wasn't really going to address the demanding of sex after an argument, because that wasn't ever really my situation, I was reallllly young when I married my first husband, and just thought it was the basic "make up sex" that everyone around me joked about and treated as normal, which if it's consensual, then it can be perfectly normal. However, if he does try to force you or coerce you into sex just to "calm him down", then that is just another form of abuse, and if it's totally against your will, it's also a crime in all 50 states since 1993.
I hope my reply didn't overwhelm you or make you even more nervous/scared. My intention was to give you several ideas & resources, not necessarily "You should do this" type advice. If anything, along those lines, the only thing I could say is "Don't wait until you're my age (46) to reach out for help and to get free from that negativity."

I'm so sorry you are going through this. I know what you mean about feeling ashamed to talk to friends and family. It's hard and becomes harder as time goes on. Its hard but find that courage to reach out and get help. That's what I'm trying to do as I work through my own issues.

Reading your post brings back some awful memories of my abusive relationship and then marriage. I am "free" now...and it makes me smile inside for finally getting the courage to say I'm done. He was mentally and physically abusing me to the point where a few times I thought I wasn't going to make it....and no one knew but his mom because I was hit, choked and pushed around very badly if i hard if I tried to call anyone during the arguments. I lost myself in the time I was with him and when I finally had 2 children that heard the abuse I felt I better get out...not for me but for my children. Don't get me wrong...he loved his kids, but found later that his life didn't really include small children. When my kids were small there was mental abuse towards them that I couldn't see going on in their lives much longer.
So....there are many details that I can go on and on about, but to help you out, I would like to give you the beat advice I can give you...and that is to get by our strength up and leave. Family is the best support for that...or as mentioned in another response... To a place that supports abused women, men and children. It is all over, but most of us forgive and forget because one small jesture of kindness was made and then it happens all over again. I know I forgave many many times and I found that after awhile apologies meant nothing...the love was completely gone and hate took over. But, deep down I loved him and always will. Sounds crazy, but I think women or anyone that has been abused find the good in people and forgive easily.
My ex has since passed away at the age of 40 and I sometimes wonder if it wasn't because of how awful he treated me.
I was married to him for 12 years so it wasn't that I didn't try, but I gave up on my marriage and on him to save myself and the most important...MY CHILDREN.
They are now 23 and 21 ...I have raised them without abuse and lots and lots of love. I have a feeling if I didn't make the decision to finally stand up for myself and leave ...I may not be reading your post and able to support others that may currently be in the same situation. Anyone that has not been through it behind closed doors can't possibly understand how it can affect "us" mentally. I know I am a much stronger person, but will always carry the awful memories when I lost myself.
Please... Reach out to anyone you can that can support you and remind you that you are worth so much more than what you are goingvthrough.
I am here ...and many others are to give you the support you need.