AITA for not giving money to my kids mom when she isn’t working?

I (40m) moved away from my ex (37f) and our kids to take a new job a couple of hours away. She was dating someone who lived pretty close to where I moved to, so I knew it was only a matter of time before she moved closer to me. We agreed that because she was only with her boyfriend for a few months, she wouldn’t move in with him. After that agreement, she lost her job and was having money issues, so she couldn’t afford a place. Her parents said she was too old to let herself get into these types of situations and refused to let her move back in with them again (she had done this multiple times before. I offered to take in the kids, and she can move into her boyfriend’s apartment, but she refused, stating, "What kind of parent would I be if I left the kids?" Umm, that’s exactly what I did for months, but I’m still heavily involved with them.

Despite our agreement, she moved in with the kids to her boyfriend’s apartment, stating it would be cheaper for me because I wouldn’t have to pay for daycare, and they would be provided for. It’s only been a month, and I’ve had the kids a couple of weekends. Now she’s demanding I give her money and is upset that I haven’t offered. She sent me a long text giving me the business, and I told her that if she asked for something, I would consider seeing what I could do. After thinking about everything, she implied I wasn’t a good parent because I moved away, moved the kids in with her new boyfriend, which I strongly opposed, and told me they would be provided for.

Before you say anything about how I’m not stepping up for my kids, I offered to have them live with me, and I would have them in daycare. Now she doesn’t have the time or money for the situation she put herself in and blames me. The kids are on my insurance, and all of the Christmas/birthday gifts they’ve gotten have been from mom and dad (to be fair, she picks them out and I buy them, so that’s true). Yes, I could easily just give her money, but I feel like she’s just looking for the easy way out and wants me to fund her while she gets everything else she wants, the kids, living with her boyfriend rent-free, and now child support from me. I don’t want to be unreasonable, but I don’t feel like I should give in to her. AITA?

UPDATE: First, I apologize for not making this clear in the original post. I am not on court-ordered child support. I would never let my kids go without, today was the first day she asked and my gut reaction was to refuse but I wanted to get some opinions, i.e. why I’m here. Second, I’m not upset that she’s living with her boyfriend. I’m happy she found someone that makes her happy, I met him once, he seems like a nice guy. That said, I met him ONCE and I didn’t want my kids essentially living with a stranger. I probably should have taken legal action sooner, that’s on me.

UPDATE 2: This was in the original post but I feel like it needs said again. I had a job opportunity that was beneficial to everyone. After taking this job I was able to pay for the kids daycare and send weekly grocery orders to them while I was 2 hours away. The kids have been on my insurance and I pay for all of their medical needs and after she lost her job, I’ve supplied literally everything for the kids. We just had Christmas and both of their birthdays within 2 months. I understand she’s struggling and I wasn’t going to try to sway the kids favor by indicating dad got this and mom got them nothing. All the presents were from both of us. There are a lot of comments about how I’m a deadbeat that I disagree with, but I understand that because I didn’t provide context how it could be viewed that way.

PROBABLY FINAL UPDATE: So I’ve tried to understand, genuinely, why I’m the AH from some of your comments. Here’s what I’ve gathered. I’ve been called a deadbeat and told I don’t provide for my kids because I’m not on court-ordered child support. It’s true, I’m not. However after I moved I still paid for 100% of their daycare and sent groceries to them weekly. This was while she was still working. When she lost her job I provided for Christmas and their birthdays. They’ve been on my insurance since they were born. Financially, I’m not a deadbeat.

Next, I was told I’m the AH because I’m not present in their lives. On a typical week, I have them 2 or 3 days, usually over weekends and it’s subject to me travelling for work. In my opinion, I have a great relationship with my kids and I talk with them every day they aren’t with me.

The last reason I’ve been told I’m the AH is because I haven’t gotten a court order to prevent the kids from living with someone that we barely know. This I agree with. I feel like I failed my kids in this regard and I plan to take action on this.

Most of the other comments are usually 1 of these scenarios or a combination of them so I won’t be replying to those. Thank you collective reddit. I honestly appreciate all of the perspectives.