My husband plays very rough with our 3-year-old daughter — chases her, tickles her and bubbles her abdomen. When they play wrestling, he does cartwheels with her, takes her out of bed hanging her upside down by the ankles, etc. My daughter has a lot of fun with those unpredictable movements with her dad, but I don’t know if hanging her upside down is okay.
It sounds like your husband and daughter have a great time together! Hanging her upside down by the ankles is alright if it’s in a safe location and for a short time — no longer than a few minutes at most. The main worry is her slipping or wriggling from his grip and falling on her head, so it’s preferable if they are over carpet or a mat, rather than over a hard surface (wood, tile, concrete, etc.).
The risk of her being upside down for too long is that blood flow is redirected to her head and away from other organs in her body, thereby depriving them of oxygen. However, this will not occur if she is only upside down for a few minutes at a time.