@BSP83,
Of course it's your business. You live in the same home. If he had extra expenses and couldn't cover rent, etc. then of course you would need to know.
So let's start from the top. Regardless of how long you have known him, don't live with him this quickly. Just ... don't. Living together changes the dynamic of a relationship, plus it creates expectations in your children.
End the living together, whether it means you leave with your kids or you ask him to find another place (and help him to do so). If he balks about leaving, give him this option -
stay and tell me everything, or live elsewhere and keep your privacy. Stand firm on this.
BTW, if this guy can't be bothered to even attempt to defend himself in court, he's probably not exactly going to be Mr. Ambitious in any other area of life. Plus there could potentially be even more kids to come out of the woodwork. Just because he thinks the more recent lady friend was sleeping with someone else doesn't mean he can't be dinged a second time for child support.
Of course having ambition isn't the be-all and end-all, but it should make you wonder if he couldn't even be arsed to find out for sure if that kid was even his.