R. - Don't feel guilty about wanting occassional time away from your mommy role! Everyone needs a breather :-)
I think you might be better finding a 'Moms Morning Out' type of thing where they offer supervised playtime from usually 9am-noon certain days of the week. I know of two mom/child playtime facilities local to Clearwater and Largo that have this a couple days a week. This will give you the break you need and take the pressure off your mother. Unfortunately she doesn't seem to really want to take care of your little one by herself, but this way yo can enjoy your mother and your daughter together when she comes over without the frustration hanging over your head that she isn't helping the way you want her too....it will make you happier and still enjoy the family time! If you really 'need' her to watch your daughter a few weeks later because you have an appt or need to do something that isn't kid friendly such as get your hair done or manicure or something then she may be much more willing since it is only occassional and your attitude will be different. Just tell her the appt is for xyz time and leave when she arrives....
As for her father....Again, you can only change yourself, not others....so, with that in mind I would still get your break by utilizing a 'moms morning out' or similar program (or friend, etc) to get the break you need. The more you expect of him, the more frustrated and disappointed you will be. Actually, I think it's awesome that your daughter gets to do things with BOTH parents TOGETHER on decent terms even though you are seperated. Not many kids in your situation get that, and it will do wonders for her emotional development. Sure, it would be nice if he wanted to see her one on one, but he doesn't, so I would just go together :-) I am sure your daughter loves it :-)