you'll need 3 x 24 hours: 24 hr for starter #1 to run its course, 24 hours to cold-crash in fridge and get yeast to floc out, then a third 24 hours for starter #2. if you want to cold-crash that, add a 4th 24 hours. you can skip that last one if you're willing to pitch all of starter #2.
there are some variables in the above. if you use a highly focculent yeast you might not need 24 hours to cold-crash. if you use a yeast with low flocculation, it could take much longer. you definitely need to cold-crash and decant between starters, since you don't have a large enough starter vessel to pitch all of starter #1 into starter #2.
can you get a larger vessel for starter #2? 1-gallon jugs can be used, depending on their bottoms and whether or not you're using a stir-plate.