Sophia
Very frankly, you can't chase your husband, whom I believe is the co-owner of the property, out of the house just because you want a separation. It is either you move out or you tell him to move out, and hopefully, he obliges your request. Alternatively, both can remain under the same roof but agree to live separate lives.
It is a myth that separation requires DOS. If he doesn't sign his agreement, you would have wasted your money on the legal fees incurred. End of the day, it may not be a wise thing to give him a surprised DOS or divorce application. Tell him your intention and get him to agree on it.
Since you have been married for more than three years, you may consider filing the divorce on unreasonable behaviour for it is far easier and faster to get a divorce approved by Court in this manner. Again, negotiate directly with him on terms of divorce so as to cut out third party costs.
As for being physically abused by him, I don't think an eyewitness account could stand alone. You need medical proof and police report on the incident. But don't take my word as final and go consult a lawyer ASAP.