It is "va" because the a in va represents he, she, and you (formal). He is going to the pool, so it is 'Mi padre va a la piscina con nosotros.'
Do use the subjunctive when you're describing your attitude towards something factual, or a fact relating to someone, provided that…
1. There are two verbs in the sentence, with a “que” in between them. ...
The 'person' of the first verb is different to the 'person' of the second verb.
-I demand a car!
1. I demand that you respect me!
2. subject + volition verb + "que" + different subject + subjunctive verb
3. Yo insisto en que ella se vaya
4. Él recomienda que comamos bien
5. Es necesario que tú hagas tu tarea
6. Yo sé que tú haces tu tarea
Therefore it's known as a noun clause. There are three reasons we would use the subjunctive in a noun clause: volition, doubt/negation, and emotion.
What is the name of the main person in this story
