Some extra tips to an already very good answer.
What are our rights?
Typically your options are a) accept as is, b) ask to be rescheduled or c) cancel for a full refund.
Unfortunately the timing here is not great. It's more than 2 weeks, so you are not entitled to compensation but it's pretty short notice to find alternative tickets.
Is this normal?
No. Rebooking after rescheduling is quite common but a two day layover isn't.
Air China offered you a very unattractive option most likely because anything else would cost them extra money. Chances are earlier Air China flights are sold out. This means they would have to put you on a different carrier, which they need to pay for.
You definitely should contact them, but there are few things you can do to prepare.
- Chances are Air China will try to steer you towards cancel/refund since this is the cheapest option for them. Figure out up front if there are reasonable alternatives and whether this is acceptable to you.
- Do not accept a 2 day layover (unless you are fine with). Use the words "unreasonable" and "not comparable".
- Search for alternative routings yourself upfront. Air China can put pretty much on any Star Alliance (Turkish, Swiss, Lufthansa, ANA, Thai, etc) flight without too much trouble. See what options are available that would work for you and specifically request the agent to book them for you. If they refuse ask "why?".
- Chances are the problem is the PEK->CPH. You can ask the agent to route you to a different airport nearby and an extra leg to CPH. Air China serves FRA, MUC, GVA, CDG, MXP, LGW, LHR, etc. There are plenty of Star Alliance flights any of these cities to CPH.
- Be friendly but firm and persistent. Having done your homework upfront can help a lot: the agents have a fair bit of leeway but they are incentivized to do what's cheapest for the airline, not what's best for you. So this will depend on your negotiation skills.
Personally I found figuring out my preferred option (plus 1 or 2 alternatives) and then asking the agent point blank about it had a good rate of success, partially you are saving the agent a lot of work, which they often appreciate.