When you say "batwings", which area specifically are you looking to get rid of? If you hold your arm out to the side, are you talking about underneath? If so:

I would do exercises to build up some lean muscle in your biceps & triceps (curls, kick-backs). Also use a really good moisturizer on your skin. I apply mine right out of the shower - and I never RUB dry, I PAT dry. These things may help...

Even with fairly toned arms, if I'm not actively flexing, I have saggy underarms, too. I'm sorry.

Get serious with hard-core exercises like variants of push-ups(whatever you can manage in whatever form - it will get better with time), pull-ups(assisted most likely until you really get strong enough)and compound exercises in general in the gym. Bodyweight exercises can be surprisingly challenging, but if you're doing weights make them heavy enough so you can do 3 sets or so of 8-10 reps(with the last couple of reps being hard). No "barbie" weights, if you get my drift. Then, on the diet front, get enough protein to build the muscles you will be getting, and eat cleanly so you will lose the fat. Many women by the time they get to middle age have very little muscle left in their arms unless they've been doing something all along. Age-related muscle loss is very real and it only gets worse as one gets older unless one gets on the stick NOW. You'll be surprised at how much you can improve your arms, and whole body in the process. Best of luck and happy training to get those good guns!:)