Actually Gabriel I think she already knows you are a good father or she wouldn't ask for so much of your imput. H rarely asks for mine.
If she didn't trust your parenting and didn't acknowledge your fatherhood role with S5, then she wouldn't be co-parenting with you.
I can understand her frustration as it's very scary being a single mother sometimes, feeling like you are responsible for the whole world and that no one will ever ask how your day has been.
I think it's also worse if there's only 1 child as with a first child, you aren't so experienced, you have a lot of expectations of your first born and if he stays an only child, he isn't off playing with his siblings, he's demanding 100% of your attention all the time.
I actually think it's easier with 4 than with 1 (having had 4 and now just caring for 1, I know) and my dd prefers it when her sisters are here.
I also understand your S5's fear. I think you did well not to get angry over her swearing at him.