Hi Ada,
My daughter and her husband have horrible allergies.
They have 2 cats and a dog.
They were tired of taking allergy meds so they bought an air purification system and now they sleep much better, have less sniffles.

In a trailer, you won't need a very big one and you take it wherever you go.
Ours has a filter that washes clean with soap and hot water.
Not expensive either.
I hope you find something that helps.
Hope