please help....

I have 2 dogs,one for over 6 yrs- the other we got 3 months ago- she is a shelter adult dog.
dog1 is high strung,foul tempered,and reactive,dog2 is sweet,lovable,and doesn't know proper dog cues for behaving.(but is great with humans)
Problem,dog1 has decided after a couple of months to fight w/dog2. AT first, no injuries,but a couple of weeks ago,dog2 fought back,and now dog1 is currently healing from an eye injury.
I have always used NILF and clicker training with dog1 and am now working on training dog2- other than keeping them separate for now,and working consistently with them on desensitizing them to each others' presence,what can I do? Dog1 learns quickly, but has a 'difficult' personality(that's an understatement)
dog2 is sweet, but doesn't learn as fast (prob. b/c she has many things to 'unlearn')
any advice here? thankfully both dogs are under 10 lbs, so keeping them apart isn't so hard, I just don't want more fighting,and I can't handle the thought of another injury.....:cry:
BTW, they're both crate trained,and love their 'beds' but dog2 is now resisting going potty outside in the yard,and that is new too.....

1. For the most part they get along well, is that correct?

2. How bad was the injury? Did the eye just get grazed by a tooth or were there multiple deep puncture wounds?

If they seem to get along well and have occasional small spats that don't escalate far I would continue to let them be together while you are around but separate when you are unable to supervise. If the fighting has gotten worse and the wounds were quite bad, you may need to look into keeping them separate except for when you directly supervise.

Is dog #2 (the friendly one?) the shelter dog?

Thank you...that's what I've been doing....I re-read my book called 'click to calm' which I used extensively with dog1- I hadn't realized there was a section on multiple dog issues.... I now keep them separated unless I'm right with them. The rest of the fam knows to use the gates,or crates when I'm not there.
I also spend a lot of time clicking/treating them both separately and together for targeted good behaviors.
so for a few weeks,no incidents...and dog1's eye is healing nicely.It wasn't a puncture wound,just a nasty scrape-
ALso now feeding them in separate bowls to reduce stress on foultempered dog1
It seems like I allowed the stress to build unknowingly (this is my guess) and dog2,while a sweetie,is now showing some problems with potty training,and over exuberant attention seeking if dog1 is anywhere nearby. (sigh) (we're seriously working on sit/stay with her right now)
So I am on square 1 with an adult dog,potty training is not easy with an adult dog!
Fortunately,they're both little,and they both love their crates...so that helps.
right now, if dog2 is loose on the deck,or in the house,she potties. When we got her,she didn't do this. ugh.