I would probably still focus on credit card 2, even though you have a longer grace period. Is there any way you can get it paid off before October? If you pay the $1700 in car repairs, the $2100 on credit card 1, and put the remainder on credit card 2, you would owe $1900. If you can get that paid off before Oct, then you would only have one credit card that will start accruing interest. I would then "snowball" these payments toward credit card 1. Either way, the more you pay off now, the less interest you will pay in the long run.
I do think an emergency fund is important, even if is only $500. Sure, $500 doesn't go a long way, but it will replace a battery in your vehicle, get your washing machine repaired, and little things like that.