Dealing directly with the owner is your best chance of getting a rental property. A management company isn't likely to take the risk. When a property is vacant for awhile the owners will only want to make sure you can make the payments.
You have a very tough case. Being self-employed is difficult enough to prove your income but when you have bad credit and you're self-employed and you have dogs it's very difficult to find a landlord that trusts you could pay rent.
You may need a cosigner someone that has good credit W-2 income and can show that they have a history of paying rent.
Actually I think your best solution would be to start fixing your credit now. Save up enough money to find an owner finance house where your credit doesn't matter as much and buy something that way you never have to worry about this again once you own your own place. Usually you can do it with 10% down +4% closing cost.
The Michael Group