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Thank you for all of your tips. This has been most helpful.
At the moment we have designed the following day routine for the rats: When we come home from work we feed them some treats, while putting our whole hand in the cage so that they can climb on it etc. Then at some point during the evening, I put a blanket on my lap and put both rats on it. If they try to run away, I try to pick them up confidently and put them back on the blanket. Later in the evening, I spread the blanket on our bed and create a sort of obstacle course for them using pillows, their own cage tubes and our worn t-shirts. They like running around in this and they often run on top of me as well, and are quite curious about everything.
I hope that doing this every day will make them feel more comfortable around us!
It's good to know that the peeing isn't necessarily nervousness, and they seem to be doing it less. I've been feeding them a mix of reggie rat food, dog biscuits, dried pasta and diced cucumber. The breeder fed them something similar (cornflakes, pasta, biscuits and some dried pellets). They don't seem to be interested in the reggie rat food, but they do eat the dog biscuits and cucumbers (sometimes the pasta, too). They are getting used to the water bottles as well, which is great!
We should be getting the new cage tomorrow or the day after, and I hope they will feel more comfortable in that because it has two levels and probably more opportunites to play. One of them got out of the cage last night again. The cage was in the bathroom because they can't get anywhere from there. However she decided to chomp on our bath mat and a leathery box/case that was on the floor. She doesn't seem to feel unwell, but I would be really angry with myself if she got sick of it. The whole cage situation is ridiculous - really not happy with the place that sold it as a rat cage. Well, soon they will be in a good cage and I hope I can provide them with the best care