First of all: His actions are not caused by you in any way or form.
This is a key factor that we always try to share with new posters: They cheat despite us, not because of us.
Second: This isn’t only emotional cheating, but financial too. Not unless the two of you have so much cash that "thousands of dollars" spent without mutual knowledge and/or consent isn’t an issue. Sort-of like I might get a Grande at Starbucks without letting my wife know...
Third – It’s your body -> your choice. Not advocating abortion, nor taking a stance on the issue of to abort or not. But at the end of the day, it’s your body and you base your decision on YOUR ethics, morals and options. Keep in mind that keeping the baby does not automatically equate to keeping this husband.
Will it be tougher raising it on your own? Yes. No doubt. But no tougher than raising a child while cohabiting with someone fantasizing about "true love" that he’s paying for. In that case, it might be more secure to have his wages garnished for child-support ahead of is payments to Wonderwoman for his fanasy-fix.
I want you to open your mind to the reality of options. Now – those options might not all be strawberries and roses, but YOU DO HAVE OPTIONS. One of those options will be the "best" – or at least the "least bad" option in moving forwards. See my tagline? I live by that. I constantly evaluate my situation, and strive to improve it. Nobody does that for me. I do it.
Why is this important? Well... Based on this being an 11 year old relationship, yet he’s furious that you "invaded" his privacy, that the finances are so separate that he can hide thousands of dollars wasted, and is "OK" doing couples therapy (albeit not enthusiastic...) then you will need to make hard choices and see if he follows.
For one, in marriage "privacy" is more-or-less limited to going to the bathroom alone. This doesn’t mean you have your nose in each others businesses all the time, but a spouse has the right to know where you are, what you are doing, maybe even why. There is privacy, as in you don’t need to know what he and his friends are talking about, but it’s a sensible privacy. Seeking sexual and emotional gratification outside the marriage is definitely not protected by some "marital privacy code".
Second: Have you two really looked into what "marriage" means in your country/state?
Sad fact is that many don’t understand the "practical" side of marriage until either death or divorce. But basically, chances are you two are one financial unit. Like... if someone scammed the card he’s using to pay Dolly online for 20k, chances are the house you two own, the vehicles you two own and so on can be collected/foreclosed.
There are all sorts of theories on how best to manage money in a marriage. Some insist on separate accounts, some on joint. What I think you need to grasp is that financial issues and differences is often listed as the most common reason for divorce. I think that irrespective of how you store money, it’s of utmost importance for financial transparency and organization for a couple if a marriage is to succeed.
Like... right now you two might be contributing semi-equally to the marital funds. But what about when you have the baby? Is it still "his" money to spend as he wants while you are at home taking care of baby?
This financial transparency isn’t about control. It’s about reaching your life-goals and creating security. It’s hard for one spouse to hide a serious issue – gambling, addiction, excessive shopping – if both are aware of income and account status.
Those thousands of dollars... That could mean a lower mortgage, less card-debt, a holiday, paint for a nursery...
Now – how serious is he about marriage?
Would he be willing to sit down and discuss things like how you two handle finances, make major decisions, share chores, intimacy and all that? Is he willing to become a husband?
Does he acknowledge how degrading and harmful these comments he’s making to another woman are to you?
