Given that this kind of test can be done by a blood draw from the mother's arm nowadays, it is a little surprising she did that procedure if it was for the sole purpose of determining paternity. But if so, it will have taken either fluid from the amniotic sac or a piece of the chorionic villi to test, and that is a much more definite test. If it gave her a positive for the other man as the father, I would believe it.
Like a lot of things, the answer is, "It depends." Did the person have testing done from tissue taken during a CVS procedure, or an amniocintesis? If so, it would be as accurate as a blood test for the baby. Did the person do a prenatal test from a blood draw from her arm and a blood test or swab from the guy? Then it would all depend on what lab was used.
The cost of a good prenatal DNA test is about $1600 to $2,000 dollars (US). There are a few good labs, they count a lot of pairs of chromosomes and are very careful. Errors that have happened have been infinitesimally small in number, for things like the man being a chimera. (In other words, a real genetic rarity.)
But because of those high price tags on the tests, a lot of charlatan so-called "labs" have entered the field, attracted by the lure of easy money. They set up in a place with little regulation, and advertise aggressively online. They cost lots less (in the hundreds and not the thousands) and panicky women flock to them. At best, they don't count many chromosomes and so their results are not reliable. At the worst, they take the money and run, they lose the samples, they forget to report back, they give a "no" to a guy when it should be a "yes." I have never heard of any of those labs giving a "yes" when it really should be a "no," however.
If you are super worried that the baby is from you, simply ask if you and she and the baby can go in person to a reliable lab and do a test. (Get a recommendation from the clerk at the family courts. They will not tell you the name of a lab whose tests could not be admitted as legal proof of paternity.) The good news about post-natal testing is that it is about a tenth the cost of pre-natal testing. You all go in, do your swabs, hand your samples to the lab tech, and that's that.
ps -- I think the baby looking like your niece is not evidence enough to worry. Lots of babies resemble each other, particularly if the group of adults involved are from the same geographic or ethnic background.