AITA not supporting another womans child financially

For a little context I am my husbands second wife. He has a child from his previous wife, 6F. We have half custody and have her on the weekends. My husbands EXwife had a son before they were together. He was an infant at the time my husband and his last wife got serious. They separated after only being together a couple of years. My wonderful husband has continued to fill the roll as father. For 5 years he's been having visits and providing for a child that's not even his. A saint this man is. Backstory over. Now we're at present day. She's remarried and has a new blended family. Struggling financially and overwhelmed with many children. The long and short is there is tax credit drama and called him a deadbeat saying he never provides for his kids. (I've personally bought them clothes, he has as well. Shoes, school supplies, medical insurance.) This hurt my husband. He told his ex wife that if she was going to accuse him of something so false he wasn't going to provide for her son anymore. Shes always using that her son is not his biochild but in the same breath the boy doesnt know my husband isnt his real father.(If anyone is the dead beat, it's the boys biodad. We have no idea who he is and really is the one who has never helped with anything. The man doesn't even know he has a son!) My husband asked me to help him stay steadfast in not continuing to enable his ex wifes entitlement. I know it's not the boys fault, he's just an unfortunate victim in the cross fire. These kids DO NOT go without. They have more than they could want and are largely considered spoiled. No harm will come to the boy when my husband recends any support. We're still letting him come over with his sister on weekends for visits but we aren't running to the store to buy him new school clothes when his mom claims he doesn't have anything that fits. We're still loving the boy and welcoming him into our lives but my husband is unwilling to continue supporting them financially. Am I in the wrong?