It's time to learn more Spanish expressions. If you have a subscription, you can click on the link below each example to learn more about the context in which they are used.
Salirse con la suya literally means "to get one's (own) way." See how the verb salir (to go) uses the reflexive pronoun se before the verb when it's conjugated (in this case in the subjunctive mood because it's used to express something that is not a fact, but a determination):
Yo no pienso dejar que esa sifrina se salga con la suya.
I don't plan to let that snob get away with it.
Caption 79, NPS No puede ser - 1 - El concurso - Part 10
Talking about determination, the phrase empeñarse en algo means to be set on doing something, to insist, to be determined:
Él está empeñado en venderos algo.
He's determined to sell to you something.
Caption 17, 75 minutos - Gangas para ricos - Part 19
As you can see, when you are saying that someone is determined to do something, you are stating a fact, so you use the verb estar (to be) in the indicative mood. However, this expression can also be used in a similar way to the expression salirse con la suya, that is, using the reflexive verb empeñarse (to insist on) plus a phrase that expresses a desire or purpose in the subjunctive mood:
María se empeña en que yo aprenda español.
María insists that I learn Spanish.
But if the subjunctive is still difficult for you, you can also use this expression to express your own or other people's determination by combining the reflexive verb empeñarse with a phrase that uses a verb in the indicative:
Mi mamá se empeña en ir al teatro.
My mom insists on going to the theater.
Yo me empeño en estudiar.
I'm determined to study.
When someone is determined to do something, it usually follows that the person will take some action, right? Well, in Spanish there's also an idiomatic expression for that:
Por favor, por favor, Padre Manuel. Usted tiene que tomar cartas en ese asunto
Please, please, Father Manuel. You have to take action in that matter
Caption 9, Muñeca Brava - 30 Revelaciones - Part 3
Maybe the origin of this phrase goes back to a time when many matters were solved by writing cartas (letters)! Surely, it took a long time to solve problems back then. Which reminds us of another expression that calls for patience and perseverance: a la larga (in the long run):
todo se arreglará a la larga
everything will be OK in the long run
Caption 22, Club de las ideas - La motivación - Part 1
Some people, however, have no patience, and such delays would just drive them crazy. For that, there's a Spanish expression that is quite illustrative: sacar de las casillas (to drive someone crazy). The word casilla is used to designate, among other things, each of the squares found in a chess board or other type of board game. A loosely literal translation of the phrase could then be: "to get someone out of their place."
¡Sí, una que me saca de las casillas!
Yes, one that infuriates me!
Caption 59, Muñeca Brava - 8 Trampas - Part 4