I'm Lucy, and I'd be happy to answer your questions today. I'm sorry to hear about your situation.
A felony on your boyfriend's record shouldn't stop him from being able to move in with you - a bigger issue might be that they'll see the unpaid child support as a debt and that might contribute to whether they're willing to allow him to live with you. Just running a credit inquiry isn't going to automatically notify the district attorney or the courts who are trying to collect child support. They'll see the inquiry if they pull his credit, just as they'll see any reported address (meaning that, if he moved in with you and changed the address on his cell phone or credit cards, or put his name on utilities, they'd still see it).
Putting that aside, I'm afraid that you haven't stated any legal basis for breaking the lease without paying a penalty. A lease is valid at the moment it's signed, and a landlord has a right to enforce it against you, even if you change your mind later. You're legally presumed to have agreed to that clause when you signed the lease, so you can't use it's existence as a reason for canceling. That means, if you break the lease, you'll still be obligated to pay the rent until a new tenant is found. You can try talking to the landlord, to see if they'll agree to let you out of the lease. That's always allowed. If they refuse, though, I'm afraid that you don't have a legal right to move out and stop paying rent. If your boyfriend moves in without the landlord's consent, they could evict you - but that's going to put an eviction on your rental history, so that's not going to help you.
The clause that you're talking about is EXTREMELY common. Most residential leases have a clause that requires a tenant to notify the landlord about extended guests and add them to the lease if they're going to be staying regularly (I've seen time periods as short as three days). And that means, even if you are able to break the lease, you could run into this same problem anywhere that you're planning to rent. I'm afraid that, even if I could give you a legal basis for breaking the lease without a penalty, that might not solve your problem. You might have better luck renting a house from a private party who's not using a pre-printed lease, but if the lease only has your name on it, ANY landlord would have a right to evict you for moving someone else into the property unless the lease says you can do it.
I apologize that this was probably not the Answer you were hoping to receive. However, it would be unfair to you and unprofessional of me were I to provide you with anything less than truthful and honest information. I hope you understand. Please rate my answer positively to ensure I get credit for the time I spend helping. If you are on a mobile device, you may need to scroll to the right. Thank you.