Should we be investing more money to visit Antarctica?

We, who?

Only if Trump decides to play hockey.

It would take ice at least a mile thick to hold up his girth.  The only place to build a suitable rink.

Only reason to do it.

Why? It wouldn't be an investment if there was no return. It's more spending.

Depends what you mean by "invest."

China is aggressively expanding its bases in Antarctica and has recently refused to cooperate with an international effort to extend existing marine wildlife refuges as protection for antarctic species against the effects of climate change.
Scientists have evidence that the ice shelves down there are melting further each summer, and not refreezing back to their previous normal size each winter. The rate of shrinkage is currently about 10% pa. This affects the land-based mammals such as seals and penguins, many of which are unique to that continent.
The warming oceans also reduce the reproduction of krill - the main food source for all marine life down there, and the only food source for several species of whales.
The size of the ice mass has an effect on global warming. Ice reflects light back into space, hence having a cooling effect for the planet's atmosphere and oceans. The less ice, the more global warming. So ceasing the emission of greenhouse gases would be an investment in maintaining the Antarctic ice cap. The US, due to its population and lifestyle is responsible for 25% of the world's global greenhouse gas emissions.
Australia, with a similar lifestyle but much smaller population is responsible for 1.5%. Nevertheless, greenies down under, like me, believe the effort to save the planet needs to include everyone, no matter how small or large.

Nobody except the U.S. has the power and resources to counter-balance China's effects down there.

I really hope you didn't mean, "should we be prospecting for coal, oil and gas in the Antarctic?"

Perhaps what you really meant was, "should we visit the Antarctic as tourists while we still can?"
I would answer no.
Every tourist adds to the cost of fuel for transport, hence exacerbating the problem of greenhouse gases.
They also tend to leave behind masses of rubbish which harms the animals and the environment.
One can appreciate the Antarctic from a distance via David Attenborough's documentaries and by visiting the animals in zoos.
And one can take one's holidays in ways and places that don't cost the earth - with no sacrifice in the level of fun and pleasure.