Nice work–I few suggestions I have:
senatus… dederunt: Unless I’m mistaken, senatus is a collective noun, so its verb ought to be singular, dedit, unless you’re going for that anacoluthonic tinge, “The Senate, they gave…”
potestatem: Hate to be nitpicky, but imperium is the proper term for authority as used by the emperor and consuls (I think praetors also). potestas is fine though.
quoniam… odissent: Needs to be cleaned up a little. Make it clear who or what the subject is. If the main verb here is odissent, it ought to be oderant. (quoniam normally takes the indicative). Also, Maximino is dative/abl., while Thracis is genitive (Thrax is an adjective meaning “Thracian” and so ought to agree with its noun, Maximino).
romanorum: To me, Romanum sounds better, as to yield the “Senate and People of Rome.” As it is, the “Senate and People of the Romans” does sound clunky. I think Romanorum occurs below again in the same way.
interficeretur: Why a subjunctive passive? “He killed them” would be a plain interfecit.
sedes… est: Reads “The seat is with an empty emperor.” A plain ablative absolute would be cleaner, sede imperatoris vacante, or in more direct, concrete Latin: imperatore absente.
uterque consules: Agreement: ought to be utrique consules. Maybe ambo might be prefered here as well, since uterque refers to “both” as in separate compacities. Did Pupienus and Balbinus take power each for themselves, or was it shared?
potestam: potestatem
invissimus: invisimi to agree w/ sunt.
autem: is not a conjunction like et, sed, at, atque… but a postpositive occuring only as the 2nd or 3rd word in the sentence. Use something like sed here.
vocavit… dicere: Are the People proclaiming Gordian emperor? If so, then dicere here is unnecessary, and a bit confusing. imperator is a 3rd declension noun, so the accusative is actually imperatorem.
interficerent: Again, why subjunctive? Simple perfect is clearer: interfecerunt.
itaque: like autem, itaque is only used at the beginning of a sentence, and watch your case on Gordianus. In fact this might be a nice place for a purpose clause: Praetoriani Pupienum Balbinumque interfecerunt ut M. Gordianus solus imperator esset (or) ut M. Gordianus solus regnaret.
potestatem…: What’s that quod doing there? And if the subject is Gordian and the senate, an et or -que is advisable. This needs disambiguation.
retinerunt: retinuerunt.
tum: tum is used to mean “then” as in “at that time.” For “then” in the consecutive sense (“this, then that”) use deinde or one of its many variants (dein, deinceps)
Gordianum: Gordianus
duxisset: duxit. Is there any question that he married her?
praefecti praetoriani: praefecti praetorio. The reason being for the dative case of praetorio here, as in the proper title praefectus praetorio, is because of the so-called ‘dative of compound verb.’ praefectus is from praeficio, “to put someone in charge of something” which takes accusative of person and dative of thing.
potesta: potestas.
questio: I prefer quaestio, but if you’re into medieval stuff then questio is just fine.
Might I ask the meaning behind this sentence?
autem: same problem as above.
per ultimo… Romae: needs a bit of clarification. How is ultimo being used here?
That’s about it. Again, nice work, just needs some polishing.