Who manufactures this bath tub faucet

Background:

All new valves sold in the USA must meet a Federal anti-scald standard meant to prevent sudden surges of hot water. A typical inexpensive 'cycling' anti-scald cartridge works on pressure only, and does not sense temperature. For example you're showering and the sprinklers go off, the cold water pressure drops, and the valve will reduce the hot flow to match. The higher pressure source is throttled prior to the mixing valve.

In addition the valves have an adjustable limit on the mixing valve: usually adjustable with a plastic ring easily accessible after installation.

A great background video on this topic, showing a Delta brand single handle faucet, is at http://www.youtube.com/watch?v=mI2NZMadb1A . The video shows the 'cycling' pressure balance mechanism in action.

A cutaway of a typical valve is at http://www.popularmechanics.com/home/improvement/electrical-plumbing/whats-behind-your-shower-walls (Popular Mechanics).

These 'cycling' valves have lots of small parts: periodic cleaning may be required.

For your situation:

• Try and rule out a strong pressure difference between hot and cold as it arrives at this fixture.
• If you can install a two handle faucet, that obviously would solve the problem.
• If your base rough in unit is a 'Grohe Flex', you can insert different single handle models in place and try them (without re-plumbing).

A more expensive 'thermostatic' valve would not have the problem you describe: it would keep the hot line fully open until a certain temperature is reached, regardless of the cold line pressure. Grohe sells such models.

It's not a great picture, but it looks like the tub is supported by wood and foam. It's possible that the wood has rotted, or the structure that supports the wood has rotted or been compromised in some way.

You can spray foam under there wildly, if you want. But if the structure that will support the foam (and tub) is compromised, it's not going to do you much good.

You're going to want to get better access, and evaluate the structure. The answer may be as simple as adding a few extra braces, or as complex as ripping it all out and replacing it. Without a better look, it's impossible to say for sure.

Since this is a mobile home, it's not likely this is a botched installation. Instead it's likely due to age, wear and tear, and/or rot.