We were looking to buy a baby stroller (3in1 set) and a bed from Italy, 1500 and 600 CHF respectively. Has anyone experience how much the customs would be for these items? Or is there a way to know beforehand (such with online calculator)?

https://duties.ch/

Deduct Italian VAT, add Swiss VAT to that. Not difficult. I doubt there will be any additional duty on a bed and a stroller.

That site doesn't let you take into account many product areas. Eg, Childrens beds might be only 2.5% MwsT (I doubt it, but it might). Otherwise, it looks fairly accurate

For sure there's no duty on furniture, just 7.7% MwsT (maybe even only 2.5% for childrens furniture) and a customs handling charge, which I can't see being over 50.00 chufs. And as you say, the supplier should deduct the 22% Italian VAT.

Deducting the italian vat is possible only if I buy the stroller/ber myself in Italy, not if I buy it online and having it shipped to Switzerland, correct? So that I can get the stamp from customs at the borders, then claim the refund.

No, it’s possible online too but the seller has to prepared to do it and not all of them are.

Recently for most of my purchases from Germany sellers did discount the VAT but haven't ordered from Italy recently. Had a sizeable purchase from Turkey recently and the did not discount...

If you are getting it shipped to Switzerland it is even easier: the seller should you apply the VAT in the first place, since the fact that the goods are leaving EU is obvious from the shipment itself.

Some don't want to do it though, in that case it's often a lost battle - so you might want to check it directly with the seller