I can tell you that learning to write in English requires a lot of effort from a seven-year-old. Some 7 year old monolingual children are still mixing up their letters at that age. I think it would be easier to focus on building up her confidence with the spoken language first and avoid the possible confusion of the two alphabets for a few years.
Do you know what age she was adopted? I can tell you that there is usually some underlying insecurity and often an extremely high concern about pleasing adoptive parents-- often more so the later the adoption occurred. (Thinking alongs the line of ¨I need to prove myself worthy of love, both to myself and to my parents.¨ They can be extremely hard on themselves.) I think it would be helpful for you and her mother to be very pleased with whatever level of performance she does in Serbian and try hard not to reinforce her overly critical view of her imperfections.
BTW, how good is her spoken Serbian, and how good is she at writing in English? If she's excellent at both, then by all means continue teaching her to read and write in Serbian. Otherwise... It may make more sense to just chat with her. She's 7 years old. When I start learning a foreign language with a new alphabet, the first thing I do is learn the alphabet. But I'm an adult! She isn't. ;-) So, maybe it would be better to just keep it low key and conversational.
Also, might it make more sense to teach her the Serbian Latin (rather than Cyrillic) alphabet...? She can learn Cyrillic later.
Obviously, I don't know the details, but the first thing that occurs to me is that the lesson may have been a tad too long for her. (7-year-olds have short attention spans. ;-) ) Or, as Kseniia said, maybe the girl was just tired. Was it an evening lesson for her? If either of these two things rings a bell, then maybe you should talk to the parents and arrange for shorter lessons at a time when the girl still has enough energy. And if her schedule is packed as it is, then maybe Antony Hoogervorst is right, and something (not necessarily Serbian, but something) needs to go.