Bluetooth Interference between piconets

Developing a workable RF communications protocol is apt to be a tricky but educational exercise. A few additional points to consider beyond what's been said:

1. On some radio hardware, it takes a lot of power to listen for a signal. With many if not most small radios, listening for a second is going to take more energy than transmitting for a millisecond; on some radios, listening for a millisecond may take more energy than transmitting for a millisecond. If current consumption is not an issue, listening continuously is a lot simpler than listening intermittently; if current consumption is an issue, however, it may be necessary to listen intermittently. Probably not a good idea until you've managed to get something going with a continuous-listen protocol.
2. Listen-before-transmit may be "polite", but it's nowhere near as useful with RF as with e.g. an Ethernet cable. Ethernet signalling is designed so that not only is it likely that a device which listens before transmitting will usually avoid a collision, but it's also designed so that a device whose transmission collides with that of another device is virtually guaranteed to notice. RF transmission offers no such promise. It's entirely possible that when P wants to transmit to Q, some other device X which is closer to Q than to P will be transmitting loud enough to prevent Q from hearing P's transmission, but not loud enough for P to notice. The only way P will know that Q might not have received his transmission is by the fact that P won't hear a response from Q.
3. It's important to beware the consensus problem--much moreso with RF than with wire signalling. If a P sends to Q, it's possible that Q will hear P's transmission and send an acknowledgment, but P will for various reasons not hear that acknowledgment. It's thus necessary to be very careful to distinguish retransmissions from "new" transmissions.

   The consensus problem can be especially vexing if one is trying to save energy by powering down receivers when they're not needed. Suppose two P and Q are supposed to communicate once every 10 seconds, so they power up and P sends Q a packet. Q receives the packet, sends his acknowledgment, and--knowing that P won't be sending anything for almost ten seconds, powers down. If P doesn't get Q's acknowledgment, he'll retransmit; since Q is asleep, however, he won't hear P's retransmission. From Q's perspective, that wouldn't matter (he's already received his data), but it means no matter how many times P retries, he'll have no way of knowing Q got his packet (at least not until the next rendezvous in about ten seconds).

4. It's entirely possible to have a situation in which node Q will be able to receive transmissions from P, but P will not be able to receive transmissions from Q. It may not be possible to usefully communicate in such scenarios, but one should at least endeavor to avoid doing anything obnoxious (like having P endlessly retry a transmission hundreds of retries per second)

As said, a workable RF communications protocol is apt to be a tricky exercise. Still, I'd expect you'll probably learn a lot from the experience.

Just because your device operates at 433 MHz doesn't mean that it's the only frequency in use in the device.

I take it you mean 'cheap' as in 'made overseas and not subjected to communication regulatory testing'. Unapproved transmitters may work well, or may not. If it causes interference with other communications, the local communications commission may get upset with you.

An approved transmitter should have this statement (or some equivalent legal boilerplate) somewhere in the manual:

"THIS DEVICE COMPLIES WITH PART 15 OF THE FCC RULES. OPERATION IS SUBJECT TO THE FOLLOWING TWO CONDITIONS:

1. THIS DEVICE MAY NOT CAUSE HARMFUL INTERFERENCE, AND
2. THIS DEVICE MUST ACCEPT INTERFERENCE RECEIVED, INCLUDING INTERFERENCE THAT MAY CAUSE UNDESIRED OPERATION."