my fiance is a stay at home dad

we have 3 kids with the 4th on the way and my two oldest are from a previous relationship (a 7 and now 4 year old). he opted to be a stay-at-home dad as the job he was at was going out of business. ive always viewed my self as a strict parent solely on the fact that i never gave my kids lavish things or bought them stuff simply bc they asked. also because when they were out of line i would place them in timeout. i would judge if i was doing a good or bad job based on when we went out in public if they were better than the other kids out. he has a far more strict approach which i didnt like for quite some time bc i was always scared of emotionally traumatizing them but when i realized after a few months it made a huge difference in my oldest i accepted it and realized i was on the wrong. however its not the same with my 4 yr old daughter. shes spoiled rotten at her dads. absolutely spoiled rotten. new clothes every visit, fast food every meal, called a princess and told shes an angel. her real father babies her so much that if i so much as look at her wrong or swat her butt he would have cps at my door to remove her. so this causes HUGE fights with my fiance and i because he is with her the most and has to deal with the effects of her being terrible. to where she now hates him. what can i do.