You’ve got a typo in there - it’s いっぱい, not いっばい.
As for ー, yes, that’s a vowel lengthener (the same one used for katakana). So when you see とーちゃん that’s her saying 父ちゃん. It’s not always a long vowel in the word itself, by the way - sometimes you see ー or 〜 used when someone stretches a vowel out during speaking, like seeing ねー at the end of a sentence, meaning just a very stretched ね (but just a ね regardless). You’ll even see manga where the line is drawn very long to indicate someone really drawing the sound out 
You can see both usages in this panel from 極主夫道 for instance:

That だーーーーー is a very long sigh, the 〜 after 疲れた is her stretching out the end of her sentence (essentially letting the sound trail off like she’s tired - 'cause she is
)
One thing to note about よつばと! is that the way characters speak is also reflected in writing. So you’ll see Yotsuba’s speech uses signficantly fewer kanji because she’s just a child, whereas her father will have more kanji in his speech because he’s an adult. This can also reflect in the use of that long vowel marker, which (I think - it’s been a while) is sometimes more common for Yotsuba and other children than for the adults around them.