A.,
You are correct; the hopping up from the table and small snacks are extremely typical for this age. You didn't go wrong anywhere, chances are that you might have gone through this at toddlerhood. (Or were still strapped into a high chair!)
Toddlerhood is a very fun, vital and active developmental process. Often, when hunger isn't calling loudly, children want to go play instead. They are exploring their world with a passion! Esp. if we discourage handling/exploring their food, they would rather get down. "Get Down!" are my 20 MO son's favorite words right now.
Some things to consider:
Allow activity but keep food in a certain area. For example, food stays in the kitchen, but your daughter can also bring a few toys in.
Allow 'tea parties' and other food-oriented play.
Place crayons and paper/ stickers and other distractions at the table.
When children have the freedom to roam instead of being strapped in, they certainly do exploit it for a time. You can safeguard from "hard to break" habits by not allowing television while eating (dreadfully difficult to correct later), not allowing roaming around the house with food, and not allowing "raiding the fridge/cupboard".
Instead, you can offer a "snack box", one that you stock in the morning with various healthy snacks you know your child enjoys. Raisins, fruit, whole-grain crackers or pretzels, a little container of yougurt or string cheese, etc. I found these to be extremely useful with little snackers because A) I wasn't an "all-day waitress" and B) there wasn't the endless discussion about food preferences. When you hear "I'm hungry", it's easy to say "Find something from your snack box". Kept me very sane during the picky eating toddler years!
One more thing: very young children don't have the same interest in sit-down meals with conversations as older children and adults do. Toddler magazines will help, and reading/looking at books and catalogs might keep their interest for a while, but really...this is just a phase. If you allow yourselves to accept that sit-down meals won't be that sort of relaxing ideal you had in mind for right now, you'll feel better about it. We've had to lower our expectations consirably. But I guarantee, if you guard against those hard-to-break habits, when your child can enjoy her conversations with you and your husband, and help set the table/prepare meals, it will be a very enjoyable experience!