Is it OK for officers to enter your home without a warrant or invitation?

My criminal attorney watched the video footage and suggested I contact a civil attorney. The officers turned their video off during the encounter and then back on. He said he got more angry every time he watched the body cam footage of the encounter. They brought five officers to my house to escort my grandkid's mother to remove the twins from the only home they had ever known. They arrested me for custodial interference. I accepted a judicial advisory plea for the charge today. My attorney said it would be better than taking the risk of a trial. I told them she could not have the twins until I spoke to an attorney. I broke the law when I told them no, I guess. The video obviously shows their unwarranted behavior. Can I get an attorney and what is the usual fee structure of such a case?