Is there any way to put a small water in her coop with her at night, at least in case you don't get out there early enough to give her a drink, she can get to it?
To integrate in a new chicken or two...is tricky in the least...they have to be kept separate for a couple weeks, then slower let out together, there is pecking and fighting, a pecking order has to be established, but once it is, it's cool beans!
Here is a pic of what I did with my 3 EE pullets...they are now a separate but together with the rest of the flock, does that make sense? They are their own flock, so to say, they rarely mingle, tired of getting pecked at, even though they are now almost full grown...
( I kept the little ones in the case, inside the coop, let the big girls outside the run, to free range, then let the little ones out to the run...then at night, put the little ones back inside the cage, and then let the older ones back inside...I did this for several weeks, they could see each other but couldn't get to each other. Its a pain, but its the only way I found, and many others, that works...)