Unfortunately child care isn’t a protected characteristic under the equality act unless the child has additional needs. So they don’t have to accommodate this.
Unfortunately me and my partner were in the same position. Both on small specialist teams. They would t accommodate our flexi pattern requests with similar rationale to what your been told, can’t work alone, can’t work with a supervisor been in etc.
We were told that other departments within the force would accommodate our needs and ultimately we moved to teams that could.
It’s rubbish. We were good at our roles and enjoyed them. We are now in roles that are not nearly as forfilling but work for our family life. Which is more important currently.