Every role player who ends up also being a parent wants her kids to learn to love the hobby, if only to have someone else to play with at home. Part of the hobby is the convention experience, and I certainly wanted my daughter to enjoy that, too.
What I found is that a role playing convention can be a great experience for the whole family, if you do a little advance planning and make some adjustments. You won't be able to play 24 hours a day for the entire convention like you did before kids.
Here are some tips I've found helpful.
Block Out Wandering Time
Plan on time to just wander the convention at your kids' pace. Don't have anywhere you need to be or anything you plan on doing, just wander. Let your kids decide what they want to see and do. That gives them a feeling of being in control in this strange environment, and they'll naturally gravitate toward the things that interest them.
For my daughter, she loved the board games and miniatures room. She saw the game boards and the miniatures set up, and immediately wanted to play. Luckily, that con had a games library, so we could try games without buying them.
Pick A Kid Friendly Con
Make sure the convention you're going to has some kid friendly activities. Ideally this would include a room with age appropriate games and toys, and some kid specific activities (face painting, charades, etc).
My daughter's first convention experience was at Origins, where they had excellent kids activities. She came to look forward to going to the kids room every day, and had her favorite games to play there.
Ensure Quality Time
If both parents are gamers, make sure the kids get time with both. One parent can take the kids on an activity while the other one plays in a game, and vice versa. One parent can also load up their late night time, after the kids are asleep.
Or, take a grandparent to serve as a baby sitter for evenings, to let both parents play.
Keep Games Short
Kids typically won't sit still for long, so when you start getting your kids into table top games, make sure they're short. Four and six hour epics probably won't work out too well for the younger gamers.
Let Them Buy Their Own Gear
My daughter loved buying her own dice and dice bag at Origins. She picked out each one individually, and put them all into the bag and carried it in her backpack. When we had a few free moments one time, I suggested we play dice, and she immediately took off her backpack and brought out her dice bag to use, all smiles.
Start The Experience Early
Don't forget to get them into the convention mood early, by playing games before going to the convention. Kids are natural role players and gamers, and it doesn't take much to encourage that tendency.
Taking your kids to an RPG convention will be a different experience than you're used to having, but it's a lot of fun and intensely rewarding. Just seeing the joy on my daughter's face at the new experiences she was having made it all worthwhile.