Edited to make more sense.

I think I'm getting warmer. In the second drawing, the two switches are physically in the same location, the light is only electrically between the switches because the wiring travels up and back.

There are only three boxes in my assumption. One with two switches, one with one light fixture and one with the other light fixture. The romexes each go to one light fixture, the old wires are the power in.

The two old wires are the power in. One is a hot and one is a neutral.

So, to make it right, connect all three neutral wires under one wire nut together first, then the rest will probably make sense. Those three neutral wires do not connect to any of the switches. One neutral wire from the panel box (old wire), one from one light box down to the switch box (the white from one romex), one from the other light down to the switch box(the white from the other romex).

That connection is the dot on the right side of the top drawing.

After the neutrals are all connected, connect two short pieces of wire to the other non-neutral wire from the old wiring. connect one of each of those to one screw on each switch.

Then, connect the two remaining black wires (one from each romex) to the other screw on each switch.

I'll make a drawing of what I'm trying to say in the morning if that doesn't make sense.