Unfortunately, all of the chemical strippers I'm aware of will attack both acrylic and oil based finishes. If dulling the gloss of the oil based finish on the table wasn't a problem, then you could remove the acrylic paint with nail polish remover. But that would also leave a dull spot on the glossy dining room table where the oil based finish has been roughened.
If push comes to shove, you can always use nail polish remover and then restore the gloss by painting highly thinne polyurethane on the dull spot, but it's probably worthwhile to try another method first:
Oil based finishes like polyurethane are much harder than acrylic water based finishes, AND oil based finishes won't soften in the presence of moisture like acrylic finishes are more prone to do. So, what I would do is dampen the acrylic paint with warm soapy water and allow that water a few minutes to soften the acrylic paint. Now take something harder than the acrylic, but softer than the oil based finish (like a wooden popsicle stick or plastic cuttlery knife) and try scraping off the acrylic paint. Hopefully, if the moisture softens the acrylic paint sufficiently, you might even be able to scrape it off with a fingernail.
SOME furniture is finished with lacquer which will turn clowdy if you leave water or a wet rag on it's surface. However, I don't believe anyone would use a lacquer finish on a dining room table which would be expected to have to endure the occasional water spill or wet place mat on it.
You can also remove the acrylic paint with any strong solvent, and ordinary nail polish remover will remove the acrylic paint much more aggressively than the oil based finish. It will, however, remove some of that oil based finish, and the result may be a dull spot on the dining room table. However, you can restore the gloss in that spot by thinning one part varnish or polyurethane with two parts white spirits (aka: paint thinner) and painting that over the dull spot. When it's thinned that much, it will self level by itself and dry to a very flat surface. However, it might still have to be polished for the surface to match the gloss on the rest of the table.
Try softening the acrylic paint with warm soapy water and scraping off the acrylic paint, and let us know how well that worked.