La forme pronominale du verbe résoudre est toujours suivie de la préposition à.

Selon le TLF, la forme « Se résoudre de » est d’un emploi vieilli. Mais il n’en explique pas l’usage.

1. A nouveau les verbes pronominaux ont souvent un sens propre, plus ou moins déductible du sens de l’utilisation non pronominale.

2. Dans on s’y résout, y est un pronom dont l’antécédent est un engagement sérieux. Dans il y va de sa fortune, y est un pronom sans antécédent, c’est un des cas où y donne un sens différent à un verbe et n’est plus réellement analysable (ça arrive aussi avec en). y aller de qqch signifie que ce qqch est en jeu.

3. Chercher des raisons autres qu’historique dans l’utilisation des prépositions est une quête vaine.

Google m’a révélé (l’existence) une réponse qui est plutôt fondéé sur décider de/se décider à, mais qui semble pertinent à ma question 3 ci-dessus, moyennant

_{p 369, The semantics of ‘empty prepositions’ in French (1996) by Kemmer and Shyldkrot, as part of Cognitive Linguistics in the Redwoods: The Expansion of a New Paradigm in Linguistics edited by Eugene H. Casad.}

Let us look at a second example of this type of situation, illustrated
in (10) with the verbs décider/se décider ‘decide’:
(10) a. Nous avons décidé de partir [sur-le-champ].    
‘We decided to leave (right away).

b. Nous nous sommes [enfin] décidés à partir.
‘We [finally] decided to leave/We [finally] made up our
minds to leave.’

Here again there is a difference in the usage Of and de. (10a) would
be most appropriate in a context with two characteristics: first, there is
little or no temporal separation between the subjects’ arriving at the
decision and the carrying out of the decision. Second, the time that it to reach the decision itself is irrelevant, although the implication here is that it was not a long process. The adverbial in brackets rein
forces these characteristics of the context, but is not really necessary;
the context given is simply the one most likely to induce In
(10b), in contrast, the temporal separation between arriving at the decision and carrying it out is irrelevant; the subjects might act on their
decision now or later, although the most neutral reading is probably
that they will do it later. In regard to the amount of time taken to reach
the decision, it is clear in this case that the decision was arrived at after a long process of deliberation. This effect remains with or without
the reinforcing adverbial enfin. The subjects had to engage in a noticeable level of cognitive problem-solving, and overcome their uncertainties before the decision was reached. More intensive and pro-
longed mental activity is therefore involved in arriving at the decision
to carry out the event specified in the infinitive clause. Hence the
appropriate English translation Of (10b) With ‘made up their minds’.
This greater level of goal-orientedness and mental participation of the
subject occurs with the use of à and not de.

_{Source: p 182, French prepositions à and de
in infinitival complements,
A pragma-semantic analysis (2008) by Lidia Fraczak, as part of Adpositions ; Pragmatic, semantic and syntactic perspectives (2008) edited by D Kurzon, S Adler}

  It is relevant to quote the interpretation given by Réquédat (1980) of some
expressions depending on whether the verb is or not reflexive-marked (e.g. refuser
de / se refuser à – “to refuse”; décider de / se décider à – “to decide” / “to make
up one’s mind”; résoudre de / se résoudre à – “to resolve”), since the author notes
the existence of some kind of dilemma in case of reflexive forms. He considers
that, for the above three verbs, the simple form does not indicate anything else
than a refusal or a decision, whereas the reflexive form implies that this refusal
or decision was preceded by a time of hesitation. The reflexive form seems also
to indicate, according to the author, the importance of the interest or of the role
of the subject in the action. As for this second remark, one may consider indeed
that whenever there occurs a dilemma or a hesitation concerning an action, as
in the case of se décider à (“to make up one’s mind”), this involves the “interest”
or the “role of the subject in the action”, or “active concern” that is mentioned by
Cadiot (1997), or “intensive mental activity”, as Kemmer and Bat-Zeev Shyldkrot
(1995) put it.