Let me just grab my dictionary... Sumere - from Sumo, Sumere, Sumpsi, Sumptus: to take, to take up, to take hold of (present active infinitive) Volo - Volo, Velle, Volui: irregular; to want (first-person singular present active indicative) Locum - Locus, Loci: place, spot (accusative case) Tuum - tuus, tua, tuum: possessive pronoun; your (neuter)
Now now, being a Latin student myself, I recognize one grammatical error in this sentence. 90% of the time, the verbs come last: "Locum tuum sumere volo."
That's not so much a grammatical error as it is just odd word order. Word order in Latin generally doesn't matter grammatically, but rather it is mixed up for emphasis. Remember that Romans didn't use punctuation or italics or bold or such shenanigans and as such relied on word order.
This odd word order would sort of be like "I want /TO TAKE YOUR/ place," I think. Although the word order you have is more standard and probably better for general-use Latin like this (it isn't advanced Latin poetry, after all).
So, grammatically correct (which is more than I can say for most people who use Latin in MLP stories), possibly awkwardly-worded.
I wouldn't exactly call this "willing", willing implies both knowledgeable, and not under duress, in this case, I think that classified as a 'wish', since she said she wanted to take the pony's place, she did, just like how Twilight granted Trixie's wishes, why the pony did not just ask Twilight to say "I wish for you're freedom, or something, however, is a point that needs to be addressed.