Yes because you are a child DOES mean that you cannot care for them like an adult can. An adult can jump in their car and drive to an emergency vet at 1am. An adult can open a credit card in an emergency situation to pay for vet fees. An adult has the last say on if an animal can be inside their home etc...
I would bring them back to your mothers house and offer to pay for all the supplies and care for their every need when you are at her house. Maybe ask if you could set up a webcam pointed at their cage so you can watch them online when you are at your dads?
Or appeal to your dad and ask him to entrust the guinea pigs decisions to your care or ask if you can live with your mom so that they can get the proper care.
Please read the links that I posted previously about the dangers of housing guinea pigs outside. Everyone always thinks it will never happen to them but believe me we get tons of posts all the time about guinea pigs getting sick outside unbenounced to their owners. Being found dead in their hutches, being ripped apart by preditors, being stolen by people, being murdered by messed up people. Believe me just because they are fine now doesn't mean they will always be fine. Something WILL happen one day and it will be the guinea pigs that have to pay that high price. We just don't want to see that happen to you. We bearly know you but we already care about what happens to your guinea pigs and you.
If you cannot provide the best of care in the best of conditions then they probably should be rehomed. Its a very hard thing to do believe me when I say it hurts LESS to rehome them then to have them get extremely sick, watch them die over a long period of time and not be allowed to bring them to a vet because of a parent or money situation.
You are still young and you can always adopt a pair of guinea pigs when you are older and have your own place! Pretty soon you are going to be into boys (or girls), clothes, music, sleep overs, after school activities and the like. Guinea pigs live for 7-9 years So in 4 years what are you going to do with them when you go off to college? Do you think your dad will care for them when you are gone? Most colleges require you to live on campus for your freshman year and there are NO pets allowed. At 4-5 years old it would be very hard on them to be rehomed. Most shelters would automatically euthanize a guinea pig that old.
I personally think teaching your mom and step dad the proper care of the guinea pigs and having them take them would be the best choice other than rehoming. But we can only tell you our opinions from our personal experince and all the thousands of post here and on Guinealynx. Believe me when I say many of us have seen and heard it all. You are not the first preteen I have posted to about divorced parents and crappy situations.
I wish you all the strenght in the world to make the right decision. Please keep us updated!