How can I replace these light switches?
First off, your brother-in-law is wrong.  You cannot attach two wires to a single screw terminal (unless it is rated for that, which most switches are not).

Here's what I'm guessing you're dealing with. Remember it's only a guess since I'm not there and you haven't supplied a picture, or drawing. 

Lets call the first switch you mentioned S1, and the other S2, then we'll use the numbers you mentioned above as the wire numbers.


Wire 4 that was attached to the screw on S2 might be power from the breaker.
Wire 2 that is connected from S2 to S1, might supply power to S1.
Wire 1 and 3 would then be switched hot wires feeding the lights.


You should also have 3 white wires connected together, and possibly 3 bare or green wires connected together.  The white wires are neutrals, one from the breaker, and one going out to each light. The bare or green wires are equipment ground, and should be connected in a similar way as the neutrals.

If I'm correct, you should connect wire 4 and two lengths of scrap wire (~6" or so) using a twist on wire connector or other approved method.  The scrap pieces of wire; or pigtails, should be made from a similar thickness and type of wire as wire 4. Next, connect one pigtail to each switch. Finally, attach wire 1 to S1 and wire 3 to S2. 

Always make sure the power is off, before working on any electrical circuit.  And if you need help, please contact a qualified Electrician.

Also don't forget. I'm not there, and I only have your brief description to go on. So I could be wrong.