I'm British, planning on moving to Gibraltar with my non-EU girlfriend who holds a 3 year UK family reunion visa.
Will she be able to make day trips into Spain without a Schengen visa?
I assume your girlfriend is a Schengen "visa national" because you wouldn't be asking this question otherwise.
She is exempted from the visa requirement only if she holds a so-called "article 10 residence card," which is a residence card endorsed "family member of an EEA national." Her family reunification visa is not an article 10 card because it is issued under UK immigration law rather than EU freedom of movement.
Therefore, Spain can and should require her to have a visa. You are in theory able to get it at the border rather than at the consulate, but that might be more of a hassle. Or maybe not. You can always try and see what happens.
The visa should be free of charge because, as your partner in a durable relationship, your girlfriend enjoys EU freedom of movement when she travels with you. The Schengen Visa Code provides a maximum validity of only 15 days for visas issued at the border (Art. 35(3)). It's not clear that this limit should apply to visas issued for travel under the free movement directive, but it still could be applied.
It's also apparent from some information here and at Travel that France, at least, would not issue a visa in this case; they would just admit the person. Spain might do the same. But if the border officers do insist on issuing a visa, it may not be useful for subsequent trips. In that case, for frequent day trips, it might be better to get a visa at a consulate, to avoid filling up the passport.
In any event. the limited validity of the visa would not affect the right to stay in the Schengen area with you, however, because the visa is only required for entry (under Article 5 of the free movement directive). The rights of residence covered in Articles 6 and 7 do not depend on the possession of a visa. In particular, the right of residence for up to three months depends only on possession of a passport. Article 6 (in full):
Right of residence for up to three months
Union citizens shall have the right of residence on the territory of another Member State for a period of up to three months without any conditions or any formalities other than the requirement to hold a valid identity card or passport.
The provisions of paragraph 1 shall also apply to family members in possession of a valid passport who are not nationals of a Member State, accompanying or joining the Union citizen.