There is no cure for the HP virus, so, the disease can still be spread even after the warts are removed.
Your immune system can fight the infection to keep it asymptomatic, but, the infected person is essentially contagious for life.
Previous infection with warts does not make a person immune from repeat infection.

You can use protection during sexual intercourse, and still, being just partially protected.
Try to boost your immune system with some supplements and healthy foods.
Ask for the HPV vaccination, it contains the two major types of HPV that causes genital warts.
By getting it, you can become protected from the other HPV type that causes genital warts, and you aren't infected with.
Regular PAP tests are important for woman with genital warts infection.

So we really are reinfecting each other?

No, you are infected and the infection stays in your body (no reinfection, reinfection happens if it is possible to clean out the infection and after a period to get it again, but, with HPV there is no cure).
One of you, was the transmitter of the infection to the other one.
If you or your partner get infected with other type of HPV that, also, causes genital warts, again, the new infection with the new type of HPV will be transmitted to the other partner.

if you are pregnant with gental warts will your unborn child have the viruse also

Genital warts also known as HPV Infection is caused by the human papillomavirus [HPV] of which over a hundred strains have been identified by doctors. One of these is Wartrol . HPV being inherently contagious has a peculiar behavior; it might be within your body for up to three months without your knowledge.