It sounds like underneath all of this trouble, you really want to do this. I would say if you want to continue,(and you think you have enough time)stick it out. Maybe sit & talk w/ the others and let them know what is going on. They all know you are new-and they voted for you, right? Tell them that you are doing the best you can, but that you might need some help, because you aren't as familiar w/stuff as they are. If you are open to constructive tips etc., let them know that too. If you let them push you out now, you will have a hard time to step back in later, imho.
As far as having to have your tots in tow- I totally feel you. I'm constantly dragging my youngest(2, almost 3
) with me to school. Juice boxes, fruit snacks & crayons are my saviors right now! Seriously, these people are (mostly) all parents and should understand. As long as they behave most of the time, it really shouldn't be an issue. I know it can be distracting, but w/low participation rates...dealing w/a couple of kiddos is worth it to me if someone is willing to step up.
Hang in there. This is a tough decision, but it's YOUR decision. Like the others said, if you decide not to continue as prez., please still be involved.