A three year break is a long time especially in some industries where the rate of change is much faster than that. You may need to scale back what role you are looking for until you get some updated experience. I have to be honest with you, a 3 year beak and only 6 years of experience is not generally what I would find as a plus in a potential hire for those jobs.
You have to have something that will make you stand out over candidates with more recent experience. You may need to get some recent training to show people you are up-to-speed or some higher level volunteer work that could show you can handle the higher level management tasks if you can find some related to the field you are trying to break back into. You will need to do a better job of selling yourself in a cover letter by really focusing in one what you have that would make you preferable to what other candidates might have.
At a mid-level management job, I would expect you might have better luck in building a network of professional contacts to get people to consider you. These jobs are often hired through the informal friends network rather than being advertised. So get out and do some work for the Chamber of Commerce or other local organizations where high level managers will be (they often support the arts too, so think about your local museum or concert hall as a place to make contacts) and get to know them and show them you can do the job through your volunteer work. Socialize and shmooze with the people you want to hire you.