Hang in there, kiddo! The fact that you are loving the patient care and working with the elderly is the important thing. Floating from unit to unit only on weekends is a tough way to re-enter though. I think your comfort level would go up much faster if you could work the same unit every weekend. You would get to know your residents and their needs and be better able to organize yourself. ASK for this...tell them you feel you will be better able to take care of the residents if you have a chance to get to know them and their needs well. They may or may not be receptive to this but you won't know until you ask.
When I first began nursing I went straight to LTC. I have always worked part-time (3 days/wk) and floated between 4 different units. I felt just like you do now! One of the 4 units was skilled care and by the time I floated back to it usually half of the patients were new to me. Eventually they asked me to work solely on the skilled unit so they would have more continuity, and although this meant working the most difficult unit, I found I actually preferred it because I could finally begin to get into a groove.
One of the things I used to do to help organize myself was make a chart before the shift began. I listed all the room #'s, patient name, had a column for BS where I put the time in if they needed a glucoscan and also wrote their BS in there after I checked it, a DNR column where I checked off all the residents who were DNR, a dressing/treatment column where I noted the time for all dressings or treatments I had to remember to do, and a big box for writing important notes about a residents condition.
When I first began the shift I did a quick round, noting residents position with a U for up, L for left side, R for right, B for back...then as I was making the first med pass I could easily see which residents had been turned and attended to by the CNA's. As you know, when you are harried doing your own job it is really difficult to supervise others. Any time you make a trip up and down the hall you can carry your chart with you and quickly update it. It becomes apparent who is doing their work and who isn't and you have EVIDENCE to back yourself up.
If your med books don't have the nice pull tabs for flagging then you can easily make your own flags by cutting out strips of construction paper. One of our nurses got a little electronic timer she called her "brain" that she would set when she was running nebulizer treatments to remind her when it was time to go back and turn it off.
Comeraderie is nice, but sometimes it is there, and sometimes it isn't. If your facility is anything like where I worked, the mix is in constant flux so hopefully that will get better with time. If your coworkers are actually hostile, then look for another opportunity. Life is too short to work with nasties.
As you get back into the swing of things, I'm betting you will feel more and more confident of your critical thinking abilities. Its tough to do critical thinking when you are feeling harried and overwhelmed. Meanwhile, do your homework...spend a few minutes each day reviewing one specific skill or condition. Little by little things will begin to gel together and one day you will suddenly realize you feel confident and in control again.