There's no extra relay besides the solenoid in the original wiring.
A little bit of a challenge to try a fix a car that's not in front of you. Since you have to go there knowing there's a problem, won't have time to fix it except small things, then need to drive it 700 miles, I'd say that's brave.
OK, if it was me that had to do it, I'd get a little prepared for the trip with some tools. Prepare to have enough to change out the starter if that acts up. I'm assuming that you will be bringing some booster (jumper) cables with you.
1, Find out something about the battery. Does it have top post or side post terminals. Bring along some sandpaper to be able to clean the terminals and cables. They need to be clean and tight. Also clean the connection where the negative cable screws onto the block. That also needs to be clean and tight. If the negative cable looks ratty, consider changing it.
2, If the car acts up you can jump the solenoid between the large positive terminal and the "S" terminal with a screwdriver (which is in your toolbox). What I would do before I left is make up a special jumper wire. Get about 6 feet of #12 wire and put an eyelet lug on it. Strip the other end of it and cap or tape that end up. When you get there, disconnect the battery and screw the eyelet end on the solenoid "S" (inside) terminal. Use some ties (bring) and run this wire up near the battery. If the key won't start the car you can use this wire to jumper to the battery (+) terminal. Remember when you do this the key must be in the ON position. Also make sure the car is not in gear and the e-brake is set.
3, I would bring a meter. With the engine running, check to see if you have at least 14 volts between the alternator large red wire terminal and ground. If the problem is, the alternator not charging the battery, you won't get far.
4, I would think about buying a battery booster. They will give you at least 1 try at starting the car. If you use it once it pays for itself. Doesn't have to be the expensive one. Get one of the cheaper ones with a light. You may need the light anyway.