A photo would help. If it's anything like ours, the frame is screwed to the wall. The screws need to go into some solid wood like a stud or other backer wood. If the screws only go into the thin 1/8" luan plywood, the frame can pull away from the wall. The factory may have missed a stud (due to poor workmanship). You may need to angle the screws to hit a stud. Screws need to be long enough to penetrate a stud but not too long so it comes out the other side and causes damage.
If re-doing the shower with new caulk, you must completely remove all traces of old silicone because fresh caulk will not adhere to cured silicone and the caulking WILL fail. For a shower stall to adjacent walls or floors, I would use 100% silicone and not siliconized caulk. For caulking around tubs, tiled showers, kitchen counters, etc., I like to use premium grade caulks (not the HD stuff) which can bought at tile supply shops and contractor tiling supply shops. A little basic info. here:
http://www.factsfacts.com/MyHomeRepair/caulk.htm Silicone makes a strong joint and is used for example, in holding glass panels in place in cabinet doors.