Basically, if you are purse carrying, you may eliminate "mouseguns" because purses are easy to conceal a fair sized gun inside. If so, your choice is narrowed down to 3 basic types of pistols;
1. Glock 26 or any double action (safe action if you are a purist) auto pistol (S&W Sigma, Springfield XD, etc)
The safe action trigger is a much shorter trigger pull than a double action revolver. It has no safety for your arthritic hands to mess with. I suggest you go with this but rent one at the range just to be sure.
2. Kimber 1911 or any compact 1911 style single action auto pistol
You might have trouble with the safety with your arthritic hands. Rent one at the range before you decide.
3. Snub Nosed 38 caliber revolver (S&W, Taurus, Charter Arms, etc)
You already stated that the double action trigger is giving your arthritic hands trouble.
4. "mouseguns"; Kel-Tec P3AT, Ruger LCP, Taurus TCP, etc.
I don't suggest that you go with a mousegun due to your willing to carry a gun in your purse. A purse can hold a bigger gun, so there are no concealability issues that would require a smaller gun. Bigger guns have less recoil and are easier to control for someone petite such as yourself.
Have fun renting guns and trying them out!
If you are forgetful of your purse and are afraid some kids may get your gun, then consider installing a smartgun on a 1911 pistol:
http://www.smartlock.com/smartgun_detail.htm
I have never used one before. I don't know if it is any good or not. If you do get one, let us know how you like it. Basically, it is a gun and you wear a special ring. The gun will not fire unless you are wearing the ring when shooting it.