To leave you need a plan.
step one is finances. See a solicitor. Do you own your house? If you do then definitely see a solicitor before you leave. divorce is a pain but you just have a google on the process and use a solicitor for the financial side.
step 2. Once you know your likely financial position you look at what you can afford for housing.
as he’s not abusive you could live in the house while it sells if you own it. You mentioned a spare room and 2 kids who presumably have rooms so the house you buy with your half of current house should be affordable as you need less rooms. spend some time in Rightmove and see how far your money goes. Decide what area you’d like to live in based on job location but also ease of social life if you are likely to feel lonely plan for somewhere with lots happening and good transport.
step 3. If the money looks liveable and you decide to proceed then you act. Tell him. Discuss how to tell the kids. Then tell wider family etc
then it’s just the practicals. If you are waiting to move till a house sells it will be a while. If you rent then it can be soon. Giving notice. Hiring a man with a can and packing your stuff. Stopping joint bills, meter readings, setting up new bills. Downsizing and dividing the furniture you likely can just make do with what you have for a while before you start changing things over time.
as others have said a dog is a positive when single and will likely help. If DH just gets home puts his feet up and is shit sexually then the dog likely will be a good stand in for company till you are single and settled and thinking of finding someone who can hold a conversation and put in effort for sex. I don’t think you should ever leave one relationship and jump immediately into another, you need processing time.
I don’t know how much mess he makes about the house but if it’s just you home most of the time the housework will be minimal, you can batch cook or do easy dinners etc. a stressful job might not feel so exhausting when that’s your only stress. Emotional unhappiness is exhausting too and you have that on top of work now.
id still try councilling before you leave. Give him the ultimatum you will leave if he doesn’t do it. If he does it and doesn’t leave it would still be good for you as it will help you be sure in whatever decision you make