First off, I am sorry this is happening. It stinks all around.
It's time for you and your husband to sit down with a marriage counselor or a therapist. This is not necessarily to try to save your marriage; it's more to figure out exactly how you are going to proceed.
Your top priority is parenting your children well. Many, many couples divorce or separate and are able to set their differences aside in order to serve the best interests of their children, who are innocent in all of it. So you don't need to stay married for them, if you don't want to. I am not pushing you to divorce or separate; I'm just saying that you can have those as options. Your kids would rather see you happy and apart than miserable and together, if that happens. And, truly, except for your newborn son, it is highly likely they have an idea of what is going on. They may not know the gory details but they are probably wondering.
Beyond parenting your children, consider your future. In particular, your financial future is something of importance. You are 34 but you still need to save for retirement. And even if your children are perfectly financially provided for, you will still need food, clothes, shelter, utilities, and medical care. If you have a job and it's a decent one, then you may be all right. If you don't, then one of the harsh realities of a marriage unwinding is that people suffer financially - and it's the person who makes less (or nothing) who will suffer the most.
And of course you are hurt and don't know who or what to believe. That is all completely understandable.
But look to taking care of your children first. Make it your mission, beyond your hurt and beyond wondering about your husband's truthfulness or what your family and friends might say. Consider that the first stop on your path, no matter what.
A marriage counselor or a therapist can help to referee this.