When entering the dwelling of a suspected mass shooter that had been armed with a semi-automatic rifle, field agents would not make the entry. That task would be the responsibility of a SWAT team.
A federal agent can and should recuse themselves from a case where a family member is involved. Sloan failing to disclose why- and being overtly hostile about it- would result in her being sanctioned by the agency for failing to perform job duties, insubordination, or both.
After Jack tells Gibbs she is recusing herself from the case, the shot goes back to Gibbs and behind him, someone in a white coat is going through a door into the hospital. Once people evacuate, they would not be allowed to go back in.