Personal "a"
 

Quiero hablar a su madre. "a" is required, yo se

A él no le gusta tomar el sol. ¿Es necesita la "A" aqui?

To him it isn't pleasing to sunbathe. Or
Sunbathing is not pleasing to him. Hence the "a"

Despues de pensando mas creo que contesté a mi propia pregunta.

Como siempre gracias.

Both are necessary.

In your first example, you're not dealing with the so-called personal a. 'a su madre' is the indirect object, and a is the preposition that introduces it. (What you want to say/speak is the direct object, by the way.)

In your second example, the preposition a is introducing the indirect object (equating to the 'to' that precedes 'him', in English).

By the way, 'sunbathing' is the subject of the sentence, in both languages. The Spanish infinitive, acting as a noun, is the equivalent of the English gerund, a verbal ending in '-ing', whose role is a noun. This ending is also found on the English present participle (as in 'He is sunbathing'), which is used to form the progressive. That equates to the Spanish gerundio (as in 'Él está tomando el sol'), used for the same purpose.

Gracias Rusty. Muy confuso pero poco a poco está empezando a tener sentido.