The Infinity Berry will fill a pet with one feed and doesn't disappear, so it can be fed to all your pets... It is a Cash Shop item..

I put my pets in the resort which feds and plays with them for a small fee.. There is the Lakeview Resort at Veta Lake which allows you to put them in for up to 21 days at a time (200sP per pet per day if you put them in one at a time or 250sP per pet if you have a Gold Account and use the 'Check All Pets In' option) or the Rathskeller Inn at Port Plunder on Omen Islands, which you need to have completed the Uncharted Land Map to have access to, which allows you to put them in for up to 31 days at at time (200sP per pet per day)