Erica,
The problem that you are reporting is not normal and since you have two units that are doing the same thing, I think perhaps you may have another issue. I would suspect either an app is causing this or your internet connection does not have sufficient bandwidth.
Since I know that Gingerbread is very stable, try this on that unit:
Reset everything to the initial factory settings by going into settings and select "privacy" and "factory data reset". Using the stock browser, try to play a flash video. If it is better, then the problem was caused by an app.
If that still does not work, bring the tablet anywhere that has free Wifi, such as a local library, etc. If it is now working, then you have a problem with your router or insufficient internet bandwidth.
If it is still not working, please send me a link to a video that you are trouble with and I will test it here.