You may be able to talk to your employer and ask about how they calculate withholding. You may be able to put into their system you have 1 dependent or more, but file without those dependent at tax time. Their system usually provides an estimate of your taxes, but it's just an estimate. There is no way for your employer to know about your other sources of income outside of your employment (hence why you file). I once worked an extra job where I only made a few thousand, and so my withholding was very small for that job. Your only danger is you might get fines for underpayment depending on the state. Also talk to an accountant, not take advice from weird people on the internet without question. :)

You can legally adjust your withholding (personal allowances) on your W4 so that your tax payments more accurately reflect what is due. Most employers allow this change every December -Januart. The IRS provides a free calculator at https://www.irs.gov/individuals/irs-withholding-calculator