But he's known her for even longer, so that doesn't explain why you have such different views on the matter.
I am in a way in your OH's boots as the parent, although in my case resident. My ex doesn't pay a penny towards our two children despite working full-time. My OH doesn't understand why I don't take steps, via csa (or whatever they are call now) to make him pay and I know that it does make him angry at times, which is understandable as he could argue that it does impact on him indirectly.
However, I do have some valid reasons (I believe!) for not doing so. The history behind it is that ex is very very bad with money and that lead to one of the reasons (not the only one) why I fell out of love with him and decided to separate. When we did, we agreed on a figure he would pay monthly. He did for 3 months until he was made redundant. Then came a serie of him having a job for a few months, then losing it again. During that time, I had to negotiate ongoingly for him to pay when he did work, each time becoming more and more stressful as he would make promises, then break them, then I would say I had no choice but to go to the csa, then he would get angry and I would get anxious and angry at any contact we would have. It is hard to express these feelings, but it left me shattered and upset and even though I am naturally feisty when it comes to my rights, working full-time and raising my kids more or less on my own was draining enough that life became easier not having this to add more stress in my life.
This added to the fact that I could see how it affected the kids. Ultimately, all they wanted themselves is being able to enjoy being with both parents without tension affecting our moods. When I confronted their dad, he became angry and resentful, and although he adores the kids, he is not very good at putting away his feelings, so ultimately, his emotions spilled out when with them, which made the visits not so pleasant for them.
When I met OH, he didn't work anyway and as contact dwindled because more and more was done through the kids, and ex probably asking the kids not to share information with me, I didn't really know if he did work or not. When I got to know that he did, I suspected it was on a self-employment basis anyway and knew that going through csa wouldn't assure any payment anyway and even if it did, he would be able to adjust his accounts to reflect a very low income. Again, it wasn't worth it. At the same time, my income increased and combined with OH's we just didn't need any additional money, even if of course, everything would be nice and there is the principle (the kids sees him every week-end).
All this to say that this has led me to decide to forget about getting any financial support for maintenance and that at times annoys my OH. It wouldn't cross his mind not to support his children if he was in that position, so it is hard to believe that ex doesn't care, and he doesn't understand my reticence to pursue it.
HOWEVER, he respects my decision. He understands my rationale up to a point and more importantly respects it. This is why I love him so much, the fact that he doesn't feel the need to impose what he believes or what he would do on me.
So maybe this is why your OH acts the way he does with you. Maybe not, just a suggestion.
PS: My OH also does things, in relation to his mum, that I would never do with my parents and also indirectly impacts on me, but I understand that it means a lot to him and I too respect the fact that I have a very different perception of the situation to him.
Sorry for the long post!