I Refuse to Carry My Late Husband’s Child, I’m a Widow, Not a Walking Uterus

I (35F) split up with my ex just over a year ago. We had some issues with getting him to provide for our son (now 8). His parents were very much interested in drama.
When I made an application through the official “Child Maintenance Service”, he received a schedule listing his monthly payments. His parents contacted me, asking me to agree to an unofficial payment plan because the CMS amount was too high. They claimed that agreeing to a lower amount between us was better than not receiving a single penny from CMS.
I refused, deciding that having this agreement on paper and not receiving it would still be better than maybe getting something.
My ex didn’t make a single payment and lost his job shortly after. His child maintenance amount was recalculated, granting him payments of £7-ish/week, which he still refused to pay, which then caused the CMS to collect the money themselves and charge him (and me) some extra fees for the service.
His parents were very much aware of it and complained about it, especially about the fees [he gets charged 20%] and about the arrears that are still on the account.
To the issue- it was my son’s birthday last week. I took time off and took him on a 2 short stay at one of the UK’s theme parks.
When his dad and his family found out, I received a call from his mother complaining that now that I live off her poor son, I can afford to take my kid to trips like this and making his dad look bad in comparison (for context, we’ve been to multiple theme parks over the years, including last year, when my ex still refused to pay a penny for his son).
I couldn’t help but laugh (in hindsight, I knew that it was immature, I just couldn’t collect myself quickly enough) and told her not to contact me about this “issue” again.
Well, she messaged me shortly after. I received a wall of text telling me off for making her son struggle, when I spent his money on memories and making myself look like the better parent. I couldn’t take it anymore and took two screenshots: Holiday booking confirmation (including hotel, park tickets, etc.) and total Child Maintenance payments received in the last year.
I sent it to her with a note: “Has your poor son sponsored our trip, or has he taken an active part in providing for our son over the last year? You can’t claim both. Pick one, please.”
In response, I received more angry messages from both ex-MIL upset about being called out like that, and from my ex, who was angry that I got his mother involved and that I pointed out how bad he is at providing for our son.
I don’t think I got her involved, but my opinion may be skewed, so here I am, asking, was it wrong of me to out him like that?
If you thought this birthday trip drama was wild, wait until you hear about the time a MIL called her own grandson a “lottery ticket”, and how a daughter-in-law made sure she had the last laugh.