This is not good, I think your marriage is in very serious trouble.
It sounds like your husband is falling in love with this woman and replacing you in his mind with her and the perfect little family they would have together where he could ride in a knight in shining armor and rescue all three of them, or so weak and conflict avoidant he won't stand up for his real family -- YOU, the one he chose and took vows with. OR
He sounds like a very nice, generous man, but this situation is out of control and I think you need to have a come to Jesus moment with him ASAP or you are going to lose him. Let's see, what do we have here:
1. The fact that he went to see the kid when he knew you were not available indicates he'd rather you not be along. He is not wanting you there for his very important experiences. That's because he's letting this other woman fill his need for family and being a parent and she's starting to crowd you out in his mind, no matter how much he loves you.
2. He is WAY too friendly with the mom. There is NO reason for 20 texts a day between them. And there is NO reason the bio mom can't be told:
"My wife and I have an agreement that we don't hang out with opposite sex people. We're making somewhat of an exception in your case because of my son, but in the future, please go through my wife for all future arrangements." End of subject.
3. He and the mom should NOT be texting back and forth even if you can read his phone. The THREE of you can have a group text.
4. MOST CONCERNING is the fact that he is telling his you that 1) Being a dad is his calling, but 2) Now is not a good time to start a family with YOU because of all the time, energy, money, etc. that he's investing in this "surprise" family.
5. Also just the fact that he's spending so much money on 3 people, 2 of whom are not even related to him. That money should be going toward the future for the two of you. And if this bio-mom has such a nice house, why is he spending all this money.
Bottom line, I've read a lot about relationships in the last few years, and it is VERY dangerous to let someone outside your marriage meet your needs. People tend to fall in love with those who they are around when they are having the most fun and the most meaningful times. Your husband may have the most innocent of intentions, but he WILL develop feelings for this woman because she's meeting his emotional needs for being a parent and being needed, etc. And it sounds like she's (unnecessarily?) around when he's with his son, which will strengthen the feelings.
The fact that he is resistant to slowing down the money, would see her w/out you, suddenly doesn't want kids with you "right now," etc. indicates he may already be falling in love with her.
I think you're going to have to put the hammer down and say "if you want me to remain your wife, these are the new rules..." YOU are the WIFE and you're being turned into the third wheel. I think you need to really start fighting for your marriage or it's going to slip away.