I am replacing two light fixtures in bathroom, they are on one switch. First one went in as planned, black to black, white to white. The second one, closest to switch, however is not looking normal. The wires came off the caps as I pulled old fixture off (screws were bent and force was required). I have two white wires twisted together, they appear to have black ink dots on them (hot perhaps?) and just a copper ground wire. There are also two black wires capped together and farther into box, I don't think these had a wire attached to them as only two caps were loose, and the black attached together wires were pretty far into box. Issue is, if the white twisted together wires with black marks are my hot power source, and I attach black fixture wire to these, what do I attach white neutral fixture wire to?
It sounds like you're not sure how this was wired up before, since the wire nuts came off when you pulled the fixture off.
There are a couple of different things that could be going on here.
You either have:
Power coming into the switch box, then going to the lights, with the switch cutting the hot wire to the lights (this is what I believe you have).
Power coming into one of the ceiling boxes with a "switch leg" running from one of the ceiling boxes to the switch box on the wall.
It looks to me as if you have power in the switch box, wired straight through the pictured ceiling box to the other ceiling box. Does the other ceiling box only 1 black, 1 white and 1 bare grounding wire in it?
If I'm right about the power coming into the switch box, then you want to:
Connect the black wire from your fixture to both black wires in the ceiling box.
Connect the white wire from your fixture to both white wires in the ceiling box.
Connect the ground wire from your fixture to both grounding wires in the ceiling box (there must be another one up inside the box, or they're pig-tailed into one wire) and connect the ground to the metal strap on that box, as well (the green ground screw). The metal parts on your fixture will be grounded when you screw the fixture to that metal strap to attach it to the ceiling.