It takes awhile for kids to hammer out the whole language thing. My 3 year old son says “cay-ent” instead of “can’t” and other variations similar to your daughter. My wife is a school teacher, and brought our son to the school’s speech specialist. The specialist said his pronunciation was developmental, and normal. It’s not an accent; he just hasn’t mastered language yet.
My understanding is that children generally develop the accent of their peers, not their parents. I’m sure accent development is a little more complicated than that, but this is the general rule from what I have read. This is especially true in my case. I don’t have an accent that resembles my parents’ at all (they have thick, Polish accents.)
However, in the OP’s case, it may just well be the young age where kids are still experimenting with reproducing the sounds they hear, with various (often hilarious) results.
Indeed, I think it’s been well established that accents come from one’s surroundings, not one’s family. My parents have thick Hungarian accents, while I have a mid-Atlantic Ameican accent. My wife’s family is even more interesting: Her parents, and everyone of that generation, have thick Chinese accents, while her generation is scattered around North America and have the accents of the area they grew up in: she herself has a midwestern accent, some cousins have a Queens accent, others a Canadian accent.
Anecdotal experience on my part shows the same. My neighbors growing up were first generation immigrants from England (not entirely sure which part off hand). They had strong accents. Their two kids, both born in the US (or in the older’s case, brought here soon enough to say “close enough”.) have bog standard accents for the North Shore of MA. (Slightly less hard-Boston)
Of course, at the age of the OP’s kids, they are still learning to pronounce correctly, so any variations are to be expected. My 5yo still can’t seem to wrap her mouth around the word “Fingers,” and have it come out as anything but “ning-gers.” She’s otherwise developmentally normal in her speech & vocabulary. There are a few words she says a bit different as well, but I expect that to change in the next couple of years.
Then she’ll be a teenager, and I won’t understand any of the cultural references, even if I understand the individual words. 
Stewie on the Family Guy show speaks with a decidedly different accent than his parents… perhaps your daughter is Pure Evil[sup]tm[/sup]?
A close friend of mine had a similar situation with her young son, he spoke with a Boston accent, even though his mother and father are both Cubans living in Miami.
They enrolled him in speech therapy in school and he now talks with a normal Cuban accent (a Miami accent actually). This was a couple of years ago, and when asked today he says he just didn’t know he was pronouncing things differently until the therapist showed him.
Too much PBS television. All the hosts seem to be from Boston.
Not at that age. If she’s Evil at all, she’s likely to be Applied Evil.
That was our daughter. Darndest thing, she had a Boston accent even though she’s never been there, knows no one from there, hasn’t had any TV affiliations, etc.
I thught it unlikely she’d picked it up from peers because as far as I can tell, most people around here don’t say “pyants” and none say "bayer.’
But this morning, I asked the lady who we leave her with during work to say “pants.” (Far be it from me to ask people weird questions out of nowhere. Anyway, knowing her, I knew she’d be game for it.)
Hearing the result, I’m guessing she’s the culprit.
As for “bayer” we’re guessing she picked that up from Grandma when we lived with her for a while.
Anyway, it’s not something I was concerned about, just curious about. I wouldn’t put her in speech therapy for this!