If our rent is due on the 15th is there a grace period?

Really depends on your contract and location as laws vary.

In most locations there is no grace period unless one is specifically provided in the lease. In some locations, such as NJ, there are laws providing a grace period for senior citizens.

When I lived in MA there was one, but it didn't mean that landlords liked it one bit, and they would just make tenants miserable and raise rents and not renew leases. So... your choice, if your state has one, how well you want to get along with your landlord. Many landlords have mortgages on their rental properties, and those payments don't have grace periods. (I've been both tenant and LL.)