The best way, unless the male is neutered, is to just separate them, but keep the cages near enough that they can still see and talk to each other. Make sure they are kept at least 6" apart or they can still breed through the bars. The bond chins have isn't really as strong as some animals where they will die without their companion, it's more like a marriage or close friendship, or in this situation, like your kid leaving home, of course they will be sad, but they will live and get over it. I would also make sure the female is in a kit proof cage (single level, 1/2" or less bar spacing, etc) and watched for pregnancy for 120 days after you separate them. Females can physically have babies their whole life, so just because she is over 10 doesn't mean anything other then the risks of complications are higher (like a woman over 60 having a baby). Another option is you can get the male neutered, but personally I don't advise it and they would need to be separated for a time anyway (I'll explain if you want but since you didn't ask I'll leave it at that). Also in case you aren't aware (some people apparently honestly don't know) just because it's mother and son does not mean they wont breed. If they were kept together in a cage that wasn't kit proof, with bars less then 1/2", it is possible they have had kits that escaped into the house and died without anyone knowing, or depending on the conditions they were living in the kit(s) could have died and were eaten. So just even if you were told they never had kits doesn't really mean they haven't or can't. It is not uncommon if conditions aren't good/right that they can be together for years without producing any kits.
Unless both males are neutered the female should never be with the males, even for playtime, but if you want to try to introduce the son to your current male personally I advise going slowly. Start with keeping them separate for 30 days, that allows any illness to show up before exposing your current chin, for the new chins to settle in, and for you to start getting to know them. After that you can move the new male's cage into the same room as your current chin, slowly moving the cages closer together. Once they are calm side by side you can start doing short controlled playtime together. If they get along you can increase the time together each time and do cage swaps to get them use to each other's scents. Once they are eating and bathing together happily you can try supervised cage time together.
