Electrical – Ceiling Light acting odd when interacted with from two switches

I think I know what's going on here, the solution is simple if the situation is as I understand it. I'll go over it again as confirmation.

The butchered wire should be the unswitched power from source that continues through the two switches, one for each light in turn, then on to the lights, then return via neutral. If you're in North America and the usual color codes were followed, this wire should be black. (Neutrals are white) The original configuration had a short length of insulation stripped from the end and attached to a switch (closet?). A few inches away, the same wire had a length of insulation stripped, but with insulation left in between the stripped portions. The copper wire itself remained continuous, the non-end bare portion looped partly around the binding screw of the other switch (bathroom?). See sketch below "Original". Only the pertinent wiring is shown, all other wiring omitted for clarity.

You then taped up the inner stripped portion and reinstalled the wire end to one switch, leaving the other without power. Correct?

If so, this is a somewhat common bad practice, mainly because the unbroken partial loop cannot be properly bound to the terminal. The fix is easy. You need a wire nut sized for 3 conductors of whatever wire gauge is used (usually #12 or #14 AWG) and two short lengths of the same gauge black insulated solid copper wire.

Remove your taped patch and cut the wire so that the entire wire is completely insulated except for the final 5/8"-3/4" which remains bare. (See sketch "Cut") Attach this and the two short pieces (ends stripped in similar fashion) with the wire nut.

The other ends of the short pieces are attached, one per switch, to where the original wire was attached. (See sketch "New") There is a particular way to make binding screw connections which you may not see in the existing work. Do NOT make a simple U bend and hook it around the binding screw, you do not get adequate surface contact this way. (Sketch "NO!")

Instead, pre-bend the wire end into a nearly complete circle, so it is configured much like an eye bolt eye. (Sketch "Yes") Re-open the end gap just enough to slip the binding screw through. The loop must go clockwise around the screw so tightening the screw closes the end gap. Before tightening the screw, pre-close the gap as best you can with needle nose pliers. Firmly tighten the binding screw and it will draw the gap the rest of the way closed.

You can see electrically you have the exact same situation, but now you have used good quality methods to achieve the connections.

This explanation assumes you are trying to control both sets of lights at the same time and not independently.

If they are on the same circuit, having separate hot wires to each switch is really redundant. The return wires from the switches are not.

There is no problem ganging both lighting fixtures on the same switch so long as the switch is rated for the power the fixtures draw. Most modern dimmers are rated 150, 300, 600 or 1000 watts. You need to make sure that the two fixtures, added together, are somewhat lower than the switch rating. If not, your gonna need a bigger switch!

All you need to do is hook one of the hot lines to the switch and cap the other hot line with a wirenut. Then pigtail both of the two switched lines (that return to the fixtures) to the switch output side. Do be sure to attach ground, for safety and to reduce the chance of random hum.

All of this assumes that the dimmers are suitable to the type of lighting (special dimmers are needed for many CFL and LED bulbs), that they are single pole (not three way), and there is no special feature requiring a neutral.

SUPPLEMENT

As Tester101 needs to regularly remind me, current code calls for a neutral wire at all switches. You have an extra wire in the switch box (the redundant hot) that could be converted to a neutral if you ever need it. You would need to switch it over at the fixture to the neutral white line, mark it at the fixture to show it is neutral (e.g., with white tape) and mark it at the switch box as neutral (also white tape).