First, for a trailer, buy used. I bought a Burly two-seat trailer for about $150 used on eBay. It wasn't new, but now eight years later it's in about the same shape as when I bought it (and now my kids are too old). If you were in SLC / Sandy UT I'd let it go for $50 but I don't have time to deal with shipping to Tx.

For bikes, you tend to pay for frame construction, components, and extras. Folding is an extra, so a folding bike of equal price to a non-folding one will probably have to sacrifice something in either frame construction or components. So if you want to be able to get the best components you can get for $400 on the best frame you can get for $400, skip folding. If folding is necessary for you, you'll have to accept lower quality in other areas to maintain the same price range.

I don't think I would buy a bike for $400 new. For $400 you can get a great used bike though. Really, a $400 bike that is ten years old, purchased new for $1000 is going to be a better bike than a $400 bike purchased new, even with modern updates.

Once you buy a bike expect to pay a little to outfit it too. If you're going 1.6 miles each way you can probably get away with using a backpack. But flat repair kit, pump (or CO2), saddle pouch for the repair kit, bike lock, new tires (used bikes often come with worn out tires), bottle cage... those are necessities. Lights may be a necessity if your commute takes place after dark. And you may decide that you would prefer having a rack and pannier.

First things first; start out simple. If the existing mountain bike you have is working well enough, just ride it. Nobody will steal it, or if they do you won't care. Work on getting lights, a flat repair kit.. those sorts of things. Later on when you find the perfect $400 deal on a bike you can migrate the equipment over. And that way you're not in a rush to buy the first thing that comes along.