Currently we have an older delta pull out single lever faucet, but many times the flexible hose that pulls out has gotten caught on dishwasher or water filter hoses, causing the hose to pop off the faucet and flood the floor! The pull out feature is great, but how can one avoid this problem with such limited space under the sink? Is there a better type of faucet to use in this situation?

There's supposed to be a weight on the hose to keep it in place.
I freed up a ton of space by getting rid of a worn out disposer. Who the heck needs those huge troublesome dinosaurs anyway. I compost now, and have very few non compost scraps.
Delta still makes very nice faucets. They can get very expensive, with 'touch' sensitive ones, and ones with multiple swivel parts, and so on, but the low priced ones are fine.

Just purchase a faucet without the "pull out" hose assembly. There are several faucets to choose from without a hose. Good luck!