So I'm going to be 21 weeks pregnant with my second when I go in a few weeks (DD is 4 1/2 so a little older). The second trimester is the easiest; actually early in the second trimester I really didn't even feel pregnant and my boss was joking that he was going to need evidence of the baby for when I took maternity leave, but in the past week or so the belly is popping and I'll be in maternity clothing soon enough... Remember the first is when you are tired for no reason (at least I've always felt that a baby that is barely large enough to be seen shouldn't be causing me to feel so tired!) and hopefully over any morning sickness you may have. Typically the second trimester is where you are just beginning to show (although by 23 weeks with your second I'm going to go out on a limb and say people will probably know you are pregnant, unless you have amazing genes!). But still your not at that super big like towards the middle and end of the third trimester so you should still be able to move around. So long as you don't have any complications everything should be fine. The biggest thing to remember is to stay hydrated, listen to your body, wear comfortable shoes, and take it easy if you have to (which is sound advice for everyone, not just us pregnant women!). Oh and you can filter the rides in each park under Accessibility & Advisories (far right) for Expectant Mother Advisories under Physical Considerations (at the very bottom of the drop down menu that will come up when you click on Accessibility & Advisories). It will provide you the list of rides that Disney and their team of lawyers have decided that "expectant mothers" be cautious of... I'm just recommending this because it seems a lot of people go through lengths to find out the list when it is readily available on-line.
I wouldn't compare 10 week to 23 weeks because they are so different; plus September while hot is not nearly as bad as August. I believe the worst would be third trimester just before your doctor cuts off travel in August; that just sounds miserable and would be a trip I'd consider delaying; by that point who wants to be walking around a theme park in 100 degree weather all day! Good luck with your pregnancy and your trip to WDW!