I have a 2009 mobile home. It has a flexible water feed line going to the toilet that freezes in very cold temps. I have been told these lines won't break if they freeze. They will just expand and when the temp goes up they will thaw out with no problems. First, is this true? Also is there anything I can do to avoid the problem? I have already added more fiberglass insulation but it still freezes.
If the line is PEX, then yes, it can generally withstand freezing. Thawing is pretty easy with a hair dryer. It doesn't take much to thaw PEX.
If the toilet shares a line with another fixture such as a sink, a simple solution would be to just open the tap and let it dribble when it's freezing out.
But if freezing is the norm for you, then you might need a bit of heat tape. Just make absolutely sure you know what kind of tubing you have before you buy and install the tape. Only a few specific varieties of heat tape are designed to work on PEX. And those that are usually have special instructions on how to install it.
The lines under the sink in my mom's mobile home have froze before. They were a clearish PEX type line and didn't leak after thawing. To thaw them, I opened the cabinet doors under the sink and aimed a small space heater blowing in. Her trailer is an older model that's had a lot of dubious upgrades over the years, but I suspect PEX type lines are probably 'standard' in trailers built today.
In your bathroom, just opening the doors under the sink to get some warm air onto more of the line may keep them from freezing in the future, otherwise you may want to run a small space heater in the bathroom over night or leave the faucet on the sink slowly dripping to keep water moving through the pipes. Even leaving the door to the bathroom open overnight may help if you don't have a heat register already in the room itself.
If your trailer doesn't have skirting around it, adding some may cut down on the cold breezes blowing across and help prevent freezing as well.