Western blot help - chromatin messing up samples

My experiment involves running a western blot on drug treated cells to measure changes in protein concentration before and after treatment. This protein is shuttled between the cytoplasm and nucleus, so I need to separate cell pellets into cytoplasmic and nuclear fractions, and then run those separately on the gel.

I can separate the fractions just fine. Problem is, the nuclear fraction is full of clumpy, sticky chromatin. I'm having trouble separating the protein supernatant from the chromatin, and I basically have no liquid to load onto my gel. Often times, the small amount of liquid I can load still has a bit of chromatin in it, which messes up the gel when I run it (I'll probe for my protein of interest on the blot and find a smear running 100 kDa in the nuclear fraction but a perfect thin band in the cytoplasmic fraction).

Any advice for getting rid of the chromatin without damaging the protein sup too much?