This is somewhat confusing. See https://www.irs.gov/pub/irs-pdf/p519.pdf for the details as to how citizens are taxed.
The biggest distinction is whether or not you are a resident or non-resident. You are a resident if you have a green card (you don't on a H4 visa) or if you meet the substantial presence test. Details on page 4, but basically if you are in the US 31 days during the tax year in question and 183 days (half a year) during that year and the prior two years (via a complicated formula).
If you are a resident of the US, you are taxed on your worldwide income. (page 17). So your overseas capital gain would be taxed. Capital gains tax rates vary based on your other income between 0% and 20%. https://www.nerdwallet.com/blog/taxes/capital-gains-tax-rates/
You also get can claim a foreign tax credit for taxes you pay overseas on the same income. In general US taxes are much lower than other countries so that often (but not always) wipes out your US tax.
You don't pay tax on the money moved, but rather the gain realized (as you describe - proceeds - cost, sometimes with slight adjustments).
You report it on your 1040 as the sale of a capital asset. Turbotax can do that for you. See https://ttlc.intuit.com/community/tax-credits-deductions/discussion/how-to-report-sale-property-abro...
If you are a non-resident, then you are only taxed on your US source income and not your foreign income.
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