Leg Training with ONLY Dumbbells?

The solution is unilateral work. Bulgarian split squats, lunges, single leg (supported) RDLs, and single leg calf raises will do the trick.

If balance is an issue, hold on to something for support. There is nothing wrong with doing Bulgarian split squat by holding DB in one hand while supporting yourself against a bench or rack with the other. 

The same goes for single leg RDL – I hold the weight in 1 hand and support myself against a squat rack or bench with my free hand. This way I'm able to focus on really stressing the hamstrings and glutes without worrying about losing my balance. My clients and I have found this to be the most brutal direct posterior chain exercise of all the deadlift variations, despite using the least amount of weight.

I wouldn't bother doing DB front squats. The legs are never the limiting factor in that movement. The back, abs, shoulders, and general awkwardness will be the limiting factor, making them a poor choice for leg development. 

You'd be best off focusing on unilateral exercises. You'll almost never be too strong for unilateral leg exercises if you have pairs of dumbbells that range up to 100 pounds or more.

These exercises will fix a lot of issues many people eventually deal with in their hips due to bilateral squatting/hinging over time (and ignoring unilateral squatting and hinging). 

Build up stability, balance and strength over time. I use well over 100 total pounds (50+ pounds per hand) with dumbbells or kettlebells on Bulgarian split squats in the moderate rep range. It can be done but takes time. 

It's going to be difficult. Especially as you're learning the exercises and finding out how bad your balance is. Again, use support if needed (I still do single leg RDLs exclusively while supporting myself against something with my off hand). 

You'll never be able to do it if you don't practice/train it. 

Dumbbells can be a true blessing for building legs and improving leg training and function if you commit yourself to the practice of unilateral leg training.

I cover a lot more about this topic in my various ebooks you can find here: https://garagegymbro.gumroad.com/?_gl=1*1ke45kb*_ga*ODcyOTg1NDIyLjE2NzU2MDk3NDA.*_ga_6LJN6D94N6*MTcyMjE5OTYzOC41OTAuMS4xNzIyMTk5NzI3LjAuMC4w