Newbie.........bridge or dslr

Recently got a Canon SX50 for Christmas. Not sure I am a fan as it doesn't do too well in action photos which the guy at Best buy did not inform me of. I have no knowledge on photography other then the regular point and shoot and sport settings on my Kodak Z950. I have been driving myself crazy deciding whether the SX50 will work for what I want or if I need to go the dslr route. I want to be able to take action shots of my kids sports and my dog (who is crazy) I originally took the rebel back because I was not happy with the zoom on the reg lens that comes with it and I didn't think I wanted to cart the zoom lens with it all the time but now I don't know if I can have the best of both worlds.

Everything I have read says that bridge cameras are not as good as the dslr for action. Is this your opinion also? And since I am totally new and not sure how far I will go with this photography interest I didn't want to spend a fortune. Is the Canon T3 an ok pick for me?

THanks everyone. I need to make a decision before it sends me into the funny farm.

Also.....When I played with the T3 I noticed the lcd screen didn't stay on. Is this just a setting or is this how it is? I like shooting from that at this point so I would want it to be on for my picture taking

Thanks!

Lisa