K.M.
Your mother and sister are such a blessing. It must be wonderful to have such a supportive family...chronic illness is tough on everyone and your mother and sister are your angels. I am unclear of what your question is, but if it is how to go forward with your divorce and keep him from seeing your son, then there are a number of things you will have to do. Washington State is a no-fault state, so you do not need a "reason" to want a divorce. It is also a community property state, which means everything is divided 50/50, unless either of you specifically have things held in your name only that were not purchased with community assets.
First, assess your situation. Aside from being separated, has he moved out of town, county, state? Where were you married (really has minimal bearing on where you choose to file for dissolution)? How long have you been married? What debts and assets do you have together? Did you file for (and/or receive) legal separation at any time?
Second, what is his relationship with your boys? If he has essentially abandoned you and your boys, then you can use that to your favor. Has he had any contact with you or your children? By phone? E-mail? In person? How often have you had contact? When was the last time?
Third, where are you planning to file? In Pierce County? Are you going to use a paralegal or an attorney? Do you think he will contest anything?
The best advice I can give you right now is to make lists of everything you have together (debts and assets), what you each now have in your possession, how you want debt and assets divided (sometimes it is better to let him keep whatever he has unless it is something really important like your grandmother's ring).
Do you have copies of your past tax returns and any paystubs, along with insurance information, where he works, what he does, etc.? Also, bank account information, vehicles and where they are registered, savings accounts, retirement info (including 401(k) and IRAs).
Go back as far as you can and make a calendar of contact with him and any vistation since separation. Put together a proposed parenting plan that reflects what you think is truly fair. You cannot keep him out of your son's life unless there are extenuating circumstances where visitation would be detrimental to your son.
I know this is a lot for you to take in, but you need to build your case the best way you can. An attorney or paralegal can help you put together a realistic scenario that will help you see this in an objective manner. If you can't afford an attorney, check out this website: http://www.tacomaprobono.org/CFLIP.html
You need to take care of yourself and your family and that includes providing the peace you need to keep yourself as healthy as possible. I do wish you the best with this situation and take care of yourself as well as you can. Please update us on this, since I am sure we would like to know that you have come out of this better off.