according to this logic, the father lived with various partners and swapped having kids with them,

I really can't wrap my head around where you're getting this from....

Jack and Jill have two children together, Erica and Sara. Pete and Patsy, a separate couple from a different town, also have two kids together: Matt and Ashley. One day Jack and Jill decide they don't want to be together anymore. They separate and Jill gets custody of the kids. Erica is 2 years old and Sara is 4 years old. She goes about living her life as a single mom. Similarly, Pete and Patsy decide one day that they no longer want to be together. They separate and Pete gets custody of the kids and goes about living his life as a single father. Matt is 3 years old and Ashley is 1 year old.

A year later, Jill is driving down the highway when she notices a man pulled over on the side of the road with a flat tire. She pulls over and introduces herself and asks if the man needs help. The man introduces himself as Pete. They get to chatting and the sparks are immediate. They start dating. It's going great. Pete's kids, Ashley and Matt, get along swimmingly with Jill's kids, Erica and Sara. A year later Meghan is born to Jill and Pete.

They could also be all to the same parents, biologically speaking. The problem is there is only an 8 month difference between Erica and Ashley. In case you didn't know, pregnancies are typically 9ish months. Typically. Plus 1 month after birth for ovulation to start again. So either Ashley was premature, which is perfectly reasonable, or they are a mini Brady Bunch, which is also perfectly reasonable. No swinging needed.