2000 Dodge Intrepid just replaced ALT. Batt diffcu start ca

I just wanted 2nd opinion! I have whats called a "maintenance free" battery it is difficult to get to u have 2 remove the wheel.I have never had aproblem w/ batt I could leave radio on for hrs get in and she start right up best luck ive ever had w/ a batt! Anyhoo let me take you where it all started! Batt light comes on so we take clean, batt new batt ends! So it didnt fix my problem then I knew it was the alternator it never went completely out cuz the car was running but wouldnt shift out of low saftey reason I suppose1 well put alt on everything was fine ran better than everi didnt have problem with batt til 2-3dy later! It doesnt matter how far I drive it leave it sitting for 30 min it gives u hard time to start! It will make clicking noise rapidly but if I turn key off then back 2 the on position wait 5sec rep.5xto start it