Ut conjunctio hîc verbo modo subjunctivo servit:
Ut has to go with mittant the subjunctive verb here, not with auxilia:
ut mittant = "that they would/should send"
ut mittant...(i) auxilia peditatûs equitatûsque vel ...(ii) auxilia peditatus equitatusque
(i) "that they should send...reinforcements of infantry and cavalry"
(ii) "that they should send..cavalries and infantries as reinforcements"—even without the "ut" the "as" can be understood but this is less obvious or natural here (in this sentence), I'd say, and the first is meant ("reinforcements of infantry and cavalry").
Verè, sine ut conjunctione fieri potest ut sensum significari cum auxiliorum vocabulo at clarior est alter vocabuli sensus ut objectum clausulae ante nomina peditatûs equitatûsque genetivo casu.
You can say the following in Latin, I do believe:
Sic latinè scribatur, ut credo:
Caesar dux milites auxilia mittit == "Caesar, the general(/as general), sends soldiers as reinforcements."
Caesar dux milites, ut equitatum ut peditatum, mittit = "Caesar, the general/as general, sends soldiers, for example [/such as] cavalry and infantry."
Caesar dux milites ut auxilia mittit == "Caesar, the general(/as general), sends soldiers as reinforcements"-->I (who am not wholly reliable) think less good but sayable more modernly with the meaning "as reinforcements" in some writers // Sic minùs benè dicitur et post classicé, nisi fallor (et frequenter erro, id fateor).
I reread your post, Paul. I imagined you read "ut" as "as" but now I see you need not have been reading it that way at all, Paul, but as in (ii) above. Sorry about that, if that is the case.
Me excusas, Paule. Epistulam tuam relegi et altera interpretatio mihi in mentem venit. Forsit tu sic dicere nolis: "ut" pro anglicè "as" suprà legi. Forsit tu exemplum secundum (ii) superum dicere vis.
I'm writing in Latin hoping for correction, and not because I'm confident in how I express myself. Latinè scribo ut ab omnibus corrigar, non quod confidenter me exprimam.