Hi Cub, no reason at all not to requeen, if you think the other queen will be superior. Just, you want to be treatment free, so ensure the new queen comes from a source that claims mite resistance. Merely being local means nothing she could have bred it from a queen she purchased anywhere.
A standard precaution when requeening if you only have a few hives, is to put the old queen aside with a few bees with a comb or two of brood, until you are sure the new queen has been properly accepted. THEN kill the old one, if that is what you want.
Or, the unit with the old queen could be your new split, if both parts have enough bees to be viable.
As to can a package be split first year? This cannot be answered yes or no because it depends. The answer is yes, if it's done right. Firstly, some packages come with the bees already carrying a significant mite load. If they go to a treatment free beekeeper, these mites will hold the package back, and make a later split less likely to succeed.
But let's say the package is relatively mite free. Then, provided the nuc has a good environment that enables it to do well, yes, a point should be reached first season when there are sufficient numbers to allow 2 healthy splits, and this may even happen faster in a TBH.
But some environments are deficient in food, ie, the bees could be short of naturally occurring nectar, or pollen, at critical periods in the hive's development. The feeding of syrup if need be, plus a pollen sub if need be, can help ensure the bees are able to fulfil their potential, and it is very likely a spring package can be split into two good units a bit later in the year.
I realise this all sounds a bit more complex than a straight yes or no would have. But that's because there are many contributing factors. Mites, and sufficient available food, are two of the biggies. There are also others. If you are looking for increase, observe the bees closely, and try to mitigate anything that is slowing them down, and you should do well.