Can someone be a monastic in their own home? If someone has the necessary financial resources and is fully dedicated to the Dhamma, would it be possible for them to be ordained as a monk yet live outside of a temple, in a place of their choosing? 

Or, on the other hand, if they do not have the necessary financial resources, but rather they live either off of producing goods relating to the Dhamma, or off of the generosity of others, but are still fully dedicated to the Dhamma, could they be ordained and live where they please?
In Mahayana traditions, there are monastics on their own (in their house, hut, living with their parents and taking care of them, etc). It is not that monks have to give everything away (savings and all) before they take ordination. As a matter of fact, both the FPMT (Tibetan Gelug) and the Kwan Um School of Korean Zen encourage monks and nuns to keep what it takes to live at least 3 or 4 years, because they are not incline to sponsor newly ordained monks. A monk is not supposed to work for a living, but it happens that the teacher encourages someone to do just that. A monk is not supposed to have debts either, but some own a loft that they bought or inherited and did not completely pay yet. A fully ordained one is not supposed to sleep in the same house as laypeople for more that four days, but some live with their parents. These are minor breaches. The most important is to follow your teacher's advises. I know of teachers who encouraged specific students to work.

For instance, in the Tibetan Gelug tradition, H.H. the Dalaï-Lama encourages newly ordained renounciates (rabjung) and novices (getsül) to stay and study at a monastery for at least 4 years. He also encourages fully ordained monks (gelongs) to stay in a monastery for 5 years after ordination. This is because he does not want unlearned monks to roam free. It makes sense, since monks are representative. He wants monks to be able to answer Dharma questions.

The short answer is: yes, it is possible, at least in most (if not all) Mahayana traditions, but I suggest you rely on a qualified teacher.