Can be done, but may cause potential problems with PoE if you intend to power the access-point via the ethernet cable. You could always look at an access-point with a passthough ethernet port on it? They seem quite common these days
As has been said, splitting the cable will limit each connection to the router to 100Mbit (which may or may not be an issue to you - it will be if you are copying files from a NAS/server at the router end and everything there is Gigabit capable for example). Personally, I'd put a decent router configured as an access point where you have your access point currently. Wireless and 4 Ethernet ports for anything that needs wiring in.
Hello, I do regular network installs, if you don't mind a small device at the computer end of things, leave that cable for a gigabit connection instead of splicing it, and rather purchase a 5 port gigabit unmanaged switch, they are about 12-15 quid. This will give you full gigabit access and you could have a party of computers if you wish.
As said, you can split the cable and simply use 2 pairs for one and 2 for the other but you are down to 100mb. Personally, I would look at a cheap Gigabit switch to split them out, unless the head end has a 100mb switch then it will.make no difference.