AHV
You have to phone/Email the AHV, they can advise. I would phone, if they try to direct you to the WEB, speak to a Supervisor tell them their WEB info is too completed to navigate!!
I think you have to leave CHF.50,000, or its transferred to the uk Social system. But any money over that you can have refunded.
I doubt, if you worked only 3 years that you've exceeded the CHF50K threshold.
BVG
Once you've left Switzerland for 2 Years, you can apply for a refund.
To get a full list of your AHV and BVG you only have to supply your AHV Nr. (on-line at AHV.ch). They then supply you with a list of all Pension funds that hold your contributions. you then have to apply to each for a statement.
If, you can get a refund, it might be worth converting/transfering all monies into one fund, this will reduce the Admin Fees.
Check-out the Swiss Banks, many operate BVG accounts and their rules may be more beneficial.You can then ask them to transfer the various monies into one fund. You may then be able to get a refund. I don't know, so ask
Or you can leave it where it is (it gains a little Interest), then if you leave the EU, you can then apply and receive the full amount. Or you can try transferring it off-shore via QROPS. This protects it from UK Tax and has other advantages. Suggest you check it out you-self.
If, in the future you return to Switzerland (presuming you've married your FianceĢ), then his/your BAV contributions may be used regarding buying a property. Also worth checking this out before getting a refund!
To be honest, if you can not get a full refund, then leave it in Switzerland. The Swiss system of AHV/BAV is, I believe better than the UK. The UK, it seems to me are trying to find numerous legal ways of robbing people of their future Pension; as they realise they can not afford to pay for it!
QROPS, is an option for both you and your husband, but it carries risk and you should check it out (and the Company).
I am considering having my UK occupation pension transffered off-shore via QROPS, inorder to avoid the 55% tax levied against any Lump-sum payment.
Hope some of this helps.