The IC you mention is a TV chip. It takes Y, C and sandcastle and spits out RGB which goes to the three cathode drive transistors. This RGB signal isn't going to come out ready to feed a monitor, it'll need attenuating + buffering first.
The sandcastle pulse is a 3 level pulse that contains back level and colour burst timing information. You can get those timing signals with a LM1881 and combine them with some transistors or cmos gates to make the sandcastle.
You'll need access to an oscilloscope to tweak the circuit and get it working properly. It'll be very difficult without one.
Honestly, I think you're better off with a more modern IC. The TDA3565 is 20 years old and there are much better devices on the market now. Have a look at the latest offerings from Philips or perhaps Sony. The CXA1585Q seems to be just what you're after - Y/C in (can strip sync off Y or external), RGB (75ohm 0.7Vpp) out, low power consumption.