Her mantra for helping kids and parents deal with frustrations is "Don't get upset, just solve the problem." I think this is excellent advice for parents. Brittany expands on this by helping us to re-frame our value judgments in Stoic context. For example, rather than thinking "My kids are fighting, I can't believe I have to deal with this again," we should just drop the value judgement at the end of the sentence.
When we look at the situation in a factually oriented way, we think the same thing, "My kids are fighting," but minus the negativity. Then we are better able to deal calmly with the problem at hand. With practice, we can implement this advice over and over to make our lives as parents easier...
Psychologically, my feeling is that it's better to empathize with kid's strong emotions before offering solutions. If we don't do that, then after a time kids to tend to repress strong emotions that are perceived as negative. These repressed emotions then go underground and become part of the unintegrated or shadow-self, which can cause problems later on - when you perceive that a part of yourself is unacceptable.
But it's also true that strong emotions don't solve problems; reason and intellect do. That is where Brittany's Stoic advice for helping parents stay calm and manage their own emotions especially shines. Tranquility Parenting is a very practical book for parents. I strongly suggest you give it read!