I don't think you should call him on it if you know he's going to deny it. And, if he knows you are on to him he'll do things to hide it better.
I'd definitely hire a PI and find out what is going on. I would also talk to a PI and find out their cost before you hire them. It would definitely be to your advantage to have proof of an affair if you are headed for a divorce. It would give you some proof to ensure you get what you need to support yourself and children.
I have had a similar experience. My husband worked with a young lady who did have a crush on him. She would send cookies and candy to my kids. She would send gifts to my kids. She actually sent a plate of Christmas treats with a card addressed to "Allen and kids" ... not me. I kept telling him that she had a thing for him and he didn't believe me. Finally, she gave him a rather expensive Christmas gift. He brought it home and showed me. I told him he needed to return it. Thankfully, he gave it back to her saying it was inappropriate. He later had her re-assigned so their jobs had nothing to do with one another. She was just so blatant about it and I'd met the girl. SO, if your gut tells you more is going on, listen to your gut.
I am so sorry for you as I can imagine how you feel. Best of luck.