We have a new mobile home. When water is running in one location and a second faucet is turned on, the water flow at the first spot decreases considerably. There does not seem to be a backflow preventer installed. Would it help to install one, or is there another solution? A corroded galvanized connector at the water meter box was just replaced, and overall house pressure seems to be good.

Pressure depends upon volume. If you don't have the volume in a making more than one draw will decrease the pressure considerably. This is caused by undersized water pipes.
A back flow preventer will not give you more pressure. I have no solution for this problem. Other than to repipe using a three-quarter main with half inch branches.
I know this isn't what you wanted to hear that this answers your question. Good luck, Tom

If you have pressure but lose volume, you may have a rust restriction, kink or other obstruction the supply pipe. The obstruction is acting as a critical orifice and only allowing so much water through. It could be a partially blocked PRV. It could also, as Tom stated, be due to insufficient pipe size.