How the heck do I engage my core and breathe while im dancing?

I know this is silly but Im having such a hard time keeping my core engaged while I'm dancing. When I do engage it, I feel like I'm not able to breathe properly. I have been practicing and can keep it engaged when I am static and can breathe fine, but when I'm dancing I am really struggling. I get lightheaded, or cant manage to engage it properly at all during fast movements. Without it I am off-balance and feel out of control. This is extremely frustrating because its preventing me from progressing on my mambo team. Does anyone have any tips for me?

I am working on strength training since my core is weak, and I do also have an anterior pelvic tilt I am working on correcting. Im wondering if those factors are hindering me a little bit.