I have just left my husband after years of abuse (associated with alcohol mostly). I had discussed how awful it was with family and close friends regularly, and I felt the same as you about feeling embaressed, and stupid to have stayed for so long.
When I fully realised the extent of the harm that he was causing, I made a plan to leave. Believe me, it took a long time to realise as I was with him for 12 years, and we had 3 kids, plus I am supposedly an intelligent professional woman who should know better....anyway, I started putting my stuff into black bin bags, and stored them in the garage, with the excuse that it was stuff for the tip/ charity shop/ having had a clear out for Xmas. I gathered important documents (passport/ utility bill/ birth certificates/ bank details) as well as copies of my DHs financial situation. I arranged to stay at my parents, who helped me move one morning when my DH was at work.
Once I had a practical plan, I felt so much stronger. I would imagine there's never a good time to go - for me it was the guilt of not seeing my DS1s first nativity as I had to remove him from nursery school.
Try to stay strong, make a plan, get support from WA, here, your family and friends, and try to focus on the fact that you are doing it to remove yourself and your kids from an abusive partner.
I was freaked out when I realised that what my DH was doing not only constituted domestic abuse, but also the emotional abuse of the children, which can actually be regarded as a category of child abuse, and could trigger social work involvement etc.
I have been at Mum and Dad's for a fortnight and the getting away was the easy part - I feel lost, etc but I know I did the right thing, so am just allowing myself the time to come to terms with it.
If your kids are at school, then the holidays it may be an ideal time to go, as you could be going to stay with friends or family, and their routine may not be as disrupted.
I know I've written all about my situation, but I wanted you to know that there are others here who are going through the same.
Please stay strong. You're not stupid, just ground down by the abuse.
Thinking of you.