What contraception were you and your secondary using? If you used a condom, then it is unlikely and I find it weird for him to react like this. It might be a somewhat extreme reaction to being confronted with the reality of having a polyamorous partner. Still, weird.
If it is possible that he is the father of the child because you didn't use contraception, then he should absolutely be able to be a father figure to the child if he wants to. The complications that brings to your married life is now irrelevant because you chose to increase the chances of conceiving with someone other than your husband. And, possible unfortunately for you, he seems to have the finances necessary to petition for a paternity test. Many men sadly don't have the luxury of being able to prove paternity.