
Rowan B. answered 08/23/22
B.A. in Classics with Latin and Attic Greek Experience
animus meus, domus meus.
animus = nominative, subject
meus = nominative, possessive determiner with gender and number agreeing with nominative subjects, "my"
domus = nominative subject
The fun part of Latin is that some words, particularly those that we attach connotations to, don't have direct translations in English. The translater has to make decisions about how they want to get the message of a sentence across. Heart and home are two of those tricky words.
While animus can be used as 'heart,' it doesn't have a direct English translation. It is also sometimes translated as 'spirit,' 'soul,' or 'mind.' For the physical body part, you might use the word cor. Cor is a neuter noun, so you would have to make meus neuter to reflect this: cor meum, domus meus.
Domus is the most common word used for 'home.' It doesn't, however, encapsulate the feeling of warmth that we associate with the word home today. A more accurate translation, therefore, is house. The idea of home doesn't really exist in a single word in Latin, so I would probably stick with domus. Ara is the word for altar, so I probably wouldn't go with that. (Though if you did, you would have to make meus feminine to match ara --> ara mea.) You could also use patria (patria mea), but this would translate closer to 'fatherland,' rather than a house.
All that is to say, there really is no one 'correct translation.' It's up to you and what you want to evoke in your translation!