It IS bizarre but part of the addiction, I'm afraid.
Before I realized there was something going on, my WH had OW pet sit once (we were on vacation) and babysit once. I later learned he sent her Victoria's Secret stuff in thanks each time, which she accepted. I threw up when I saw the invoices. She hasn't been in our house since.
Ken, I'm with Allen. Put a stop to this NOW. No contact means NO CONTACT with OM, OMW, OM kids, NOTHING! Don't let her pull the "but it's just a harmless little birthday party!" card. There IS no justification for continuing to harm a marriage.