Husband and another woman!!!

The fact he didn't tell you he was going on a date with this woman speaks volumes.
You need to have a serious conversation with him about appropriate behaviour and boundaries when he is supposed to be in a monogamous marriage with you.
Even if this is so far just friendship it has all the potential for developing into something serious between them.

He’s being clueless and insensitive at best, or straying under the guise of an innocent sporting interest. In your situation I’d go to a few of these meet-ups, there is a possibility that it’s completely benign, and they really are just friends (I have several very good male friends, platonic relationships do exist) but you need to reassure yourself one way or another. Banning him from seeing her is not really the answer, have a conversation about trust, and acceptable behaviour.

I dont know, some of these responses seem extreme. The fact that he brought the kids and posted it on social media means he's not sneaking around or trying to hide anything. I wouldn't immediately jump to affair.

If you're not comfortable with it, talk to him camly. Explain how you feel. I wouldn't react well if my partner started dictating who I could be friends with. It's controlling and borderline abusive.

Unless you're going to drip feed that he has a history of cheating. In which case get rid. You cant spend your whole life watching his every move. You either trust him or you dont.

Well I'll start from my firm belief that MEN CAN'T BE TRUSTED.
But here, I mean wtf?
There's obviously SOMEthing going on - I'm not suggesting it's necessarily a 'worst case scenario' as it sounds as if your children are usually with them.
But you're certainly right to be suspicious and want to thrash out any wrongdoings.
Sorry I should have started by saying that I feel sorry for you.

Your not happy with him spending time with another woman, believe me not many would be and taking your children to meet her (pretty disgusting). He knows your unhappy about it but it means more to him to keep her happy and meet up on “dates” when he sould be engaging/watching your children he chatting/lunching etc with her (poor kids they must have felt awkward with daddy and his girlfriend. Nip this in the bud & tell himand her it’s not on. His response to this will be telling is he really willing to give up his wife & kids for someone he met at a sports event. Tell him to get real. This has emotional affair written all over it

No it is not OK.

Just taking a wild guess she's younger, attractive and possibly "could do with friends/going through a tough time". This needs to end now.

You're clearly not being paranoid. What a thing to do!! I think you have to use this anger, cards on the table, he categorically doesn't see her again. Blocks her on everything. And request full transparency as to how this all came about.
Then you decide what you want to do, based on his responses. At the moment, he's hoping you'll back down and let him continue whatever this is.