sibling aggression-brothers

Question
I bought 2 brothers from the same litter at the age of 6 weeks.  They are now 4 months old.  Their playful romping has turned into growling, attacking, biting, aggression.  I had them neutered, that seems to make no difference.  I separate them in their own cages when they become aggressive.  That only solves the problem for the moment.  They fight over possessions, chew toys, chew bones, food, etc..  Taking away the object that they are fighting over does not stop the aggression either.  Is this just a puppy phase that they will outgrow with maturity or is it just going to get worse?  What should I do about it.  I exercise them outside playing fetch.  They do that very well.  I have considered getting rid of one of them to solve the problem, but I don't know which one.  It would break my heart.  I am an older lady with hip, knee, and back problems.  I have a tendency to fall.  So, I need a gentle dog.  This aggression could cause me a serious health  problem if it causes me to fall.  I need help with this problem.  Thank you.  Ellen

Answer
Ellen, they're doing this because "the pack leader" hasn't taught them it's unacceptable.
So now we need to do that :)  

I'm going to teach you the easiest way to stop this in its' tracks BUT you need to do it consistently.

Get a bunch of empty pop or beer cans...put about 15 pennies in each one and tape tops shut.  Have them within reach "everywhere".

The FIRST SECOND any aggression starts, pick the can up and say NO and bring it down hard once...(sort of like throwing a baseball but, of course, don't let go).

This makes an incredible noise to dogs since their hearing is about 50 times more sensitive than ours.

After they've stopped...stand perfectly still, look right into their eyes and say NO again.  If either one even makes a slight move to continue...bring the can down again.
Say NO again and move towards the offender.

Doing this plus "moving at them" is a huge message.

No praise - no pets when they stop.  Walk away.  The pack leader has spoken.  It's over.

What's happening here is they're both male and fighting for top dog status.  Your job is to impress on them that they are BOTH members of the pack and YOU are top dog.

At this age it's not hard to break these habits.

So do try this and let me know the results and depending on what you tell me, we'll go on from there.

don't give up, Ellen...it doesn't take strength or muscle to control dogs.  It's attitude that counts.
Delores