Hmmm .. is there any particular reason why the clinic is going to ICSI instead of IVF? Since you have been able to get pregnant naturally (even though
those pregnancies have not been sustained), it would seem that there is no problem with your partner's sperm?
Your instincts sound about right (incidentally, my clinic did a trial with one lady, who had had a child a very long time ago, but kept miscarrying while trying to conceive her second. When testing her genetically, they found a chromosomal defect - I think 7 and 13. So they did a stimulated cycle with IVF and also did PID / PGD. They managed to have 5 blastocysts that were tested and interestingly enough, the first had two chromosome abnormalities, 7 and a different one. The second had three chromosome abnormalities; 13 and two others. The third and fourth had abnormalities all across the board - but neither 7 nor 13 were impacted. The fifth was a perfect blast that was transferred and ended up becoming her baby). Our doctor showed us this to demonstrate, that even if you have no chromosome abnormalities / have them - the combination of male and female DNA when making the baby can still have an entirely different outcome... (and also why your Mum and Auntie have been able to have two children each).
It may well be that your genetic issue is contributing, but I wouldn't be entirely convinced that it is the only contributor and think that your idea to have other testing done is a very good idea. It doesn't seem to be an implantation issue, as you have been pregnant a few times. It doesn't seem to be a sperm issue, as fertilisation doesn't seem to be a problem. You know of your genetic translocation (I just read up on it and it does seem to be a major contributor to miscarriages) so it does make sense to have IVF done with the genetic testing ...
Unfortunately, as so many of us have experienced, even having a perfect specimen transferred does not guarantee that a baby will be the outcome - but with the PID, your chances should be quite good.
What other tests are you thinking of having done?
xxx