If we bought a trailer home but the people we bought it from won't move out and we have the title legally, can we shut the power off?

No, you may not shut off the power. The law does not allow "self-help" evictions, or trying to drive former tenants, owners, etc. out by turning off utilities, changing locks, etc.

What you can and should do is bring a legal action. You can only evict through the courts, but if you have title and they do not have any right (e.g. any lease) to stay there, the case should be fast and straightforward. You can also sue them for monetary compensation, such as for the cost of utilities, taxes, and mortgages during the period they are unlawfully occupying your trailer.