1. Your wife is correct. DL will get you to DCA. But, the issue is when.
2. Only you can assess whether the meeting is important.
3. Don't count on SDC. Last flight of the day picks up all the prior misconnects so it's often full, esp. inbound intl. flights where DL knows it's got a problem hours ahead.
If missing the 9:00 AM meeting is OK, go ahead and chance it. If it isn't, you need a fix now. Also, remember that unless the reason for a delay is MX, you will pick up the cost of a hotel.