According to Rav Mordechai Eliyahu, a woman could immerse bein hashmashot on Friday night. This is the time between sunset and tzet hakochavim (nightfall, when the stars come out). As a Sefardi woman, you could certainly follow this psak, but check the mikveh hours, as Friday night hours are usually short.
You could meet your husband at shul even before tzet hakochavim, as long as you arrive at home only afterwards. If you are at the mikveh early and are the first one to immerse, there should still be plenty of time before shul is over, and you probably won't keep your husband waiting very long. If it is a real problem to take the kids to shul, you could leave them with a neighbor or friend as well. It is halachically preferable for tevilah to be private, but under special circumstances you could tell someone, if it will help you fulfill this important mitzvah.