I am familiar with the simile of the two arrows, i.e. an unenlightened being experiencing physical pain (first arrow that hits) will grasp for the release from that pain and thus be hit by a second arrow. Since feelings are conditioned (anicca) like the body, there must be a "first arrow" made of feelings/vedana. So i guess, even the buddha himself had to experience sadness. But there was no grasping towards the a different state of feeling. That also goes for painful mind objects like "the concept of your mother's death", which might give rise to suffering. In the past I thought that an arahant has to be free from bad feelings, but i guess now that this is not the case at all. This did not come out as a question, which this site is for. Anyways, what do you think?
A feeling like sadness would have to come from attachment to some sort of mental construct, right? Sadness does not come out of nowhere.
For example, a regular person might think: "my mother was around since the day I was born, how can it be that she is gone forever!?" Cycling this thought and various memories over and over he or she experiences a feeling of sadness.
Now, a Buddha is famously beyond conceptual boxes, their mind is not boxed. Because it's not boxed, how could something like sadness arise?
For example, if the Buddha's mother died, in Buddha's mind there's no circling of the idea "my mother is dead, this cannot be" etc. Buddha knows how in the stream of phenomena individual appearances arise, morph, and cease. Buddha knows that mothers and other sentient beings are born and die.
Rather than their deaths, what's important is whether their lives were meaningful in the grand scheme of things, or were they entirely consumed by the petty samsaric activities. If they were consumed by the petty samsaric activities, which are fruits of the previous karma of ignorance and are themselves the karmic seeds of future ignorance, that in the Buddha's mind is a reason to experience compassion and motivation to help all sentient beings move away from cycling in samsara and towards awakening and liberation.
In other words, the Buddha's mind is purified and likewise the Buddha's feelings are purified, too. Instead of sadness the Buddhas experience understanding and compassion.
That said, Buddha clearly appreciates the importance and value of relative relationships, so he/she would absolutely pay all the customary deep respects to the mother, both while she is alive and in connection with her death.
So, to answer your question, no, I don't think the "two arrows" concept applies to Buddha's emotions, I think it applies to physical feelings, where the first arrow obviously remains and the second arrow is gone.
The sutta clearly says that the two arrows refer to physical (kāyika) and mental (cetasika) feelings (vedana).
The educated noble disciple (ariyasāvaka) experiences painful physical feelings, but he doesn't "mentalize" it. Hence, he is struck only by painful physical feelings and not painful mental feelings.
That means, he is struck by one arrow and not two, unlike the uneducated ordinary person (puthujjana), who is struck by both arrows.
When an educated noble disciple experiences painful physical feelings they don’t sorrow or wail or lament, beating their breast and falling into confusion.
Sutavā ca kho, bhikkhave, ariyasāvako dukkhāya vedanāya phuṭṭho samāno na socati, na kilamati, na paridevati, na urattāḷiṁ kandati, na sammohaṁ āpajjati.
They experience one feeling:
So ekaṁ vedanaṁ vedayati
— physical, not mental.
kāyikaṁ, na cetasikaṁ.
It’s like a person who is struck with an arrow,
Seyyathāpi, bhikkhave, purisaṁ sallena vijjheyya.
but was not struck with a second arrow.
Tamenaṁ dutiyena sallena anuvedhaṁ na vijjheyya.
That person would experience the feeling of one arrow.
Evañhi so, bhikkhave, puriso ekasallena vedanaṁ vedayati.