I've just completed Dead Money, and I go try to get Rex/ED-E and I hire them, I step outside the building or wait 5-10 seconds, and it says they leave and go back to Primm/Freeside. I want to do all the companion sidequests, but this is going to ruin that if I can't fix it. Any Help?

Rex and Ed-e cannot both be in the party at the same time.

Both are critter type followers.

Its the same problem one would have trying to have 2 human followers, and the same limitation.

Work with only one critter and one human/humanoid follower(s) till their quest is complete, then move on to the next.

No no, You've misunderstood. I don't mean I try to hire them both at the same time. I try to hire one, and he just leaves me seconds after, regardless of if I have a companion with me or not.