Draupadi
The Princess of Panchala known with her another name Draupadi (being daughter of Dhrupad) was born from Yajna fire and was a very intelligent, illustrious, hard working and wise lady of her time. When Satyabhama asked her how to make Krishna her only as she saw Pandavas being very respectful to her, she teaches her the qualities of why she was respected and loved by her husbands. She was a very hard working lady and a large part of administration and Antahpura was looked after by her and she was the one who helped her husbands manage such a big kingdom. Without her support, the Pandavas would have suffered difficulty in making Khandavprastha to Indraprastha. Even when she was grossly humiliated in Gambling place by Duryodhana, Dushasana and Karna, she first tried to save her honour and then she saved her husbands. Even Karna praised her quick thinking and intellect. She had not said Andheri Ka Putra Andha in original Mahabharata, neither she stopped Karna from participating in her Swayamvara. Both stories comes from later interpolations. These are not accepted as composed by Ved Vyas and were later added and therefore removed by scholars from their editons.
Draupadi was not a lady who would insult her guests, she was extremely wise and learned.
Kaikeyi
Kaikeyi was Princess of Kaikeya Kingdom and daughter of King Ashwapati. She was an excellent chariot driver and a horse rider. Maharishi Valmiki calls her Tejaswini (Brilliant). She had saved her husband Dashrath in war against demon Sambhar. Kaikeyi was taught many skills including war skills.
Kaushalya, first wife of Maharaja Dashrath was an administrator and many villages came under her. This fact was said by Laxman to Shri Ram when he was worrying how his mother would be able to live without him and having no one to protect her. Laxman said she is protecting and providing for people of many villages, she would be able to take care of herself. Also, Shri Ram hoped that Bharat would be caring for Kaushalya as Shri Ram never did anything to hurt Kaikeyi.
It can be inferred that Princesses were given proper education so that they could become good mothers, intelligent queens and also learnt warrior skills for self defence.
Kumudvati
Naga Princess Kumudvati, Chief Queen of Kusha had tremendous agency because she had wished to marry Kusha and even told her wish to her brother, Naga King Kumud. It shows that Princesses could easily express their desires to their families. Kusha was more than delighted to have gotten such an intensely passionate and devoted queen. Her personality is a little far fetched and can make feminists uneasy because her entire personality revolved around her husband and caring for their children. But that was her choice, this wasn't forced upon her. She was also a staunch devotee of Lord Shiva and Kusha had built Nageshwarnath Temple for her near Sarayu river.
Kusha's first wife Champika had birthed nine daughters but she had no sons. Yet, she enjoyed a very respectful place in his palace. Champika was a pillar for initiall reign of Kusha in Kushavati and gave him emotional stability from trauma of losing his mother. Despite having no sons, Champika was respected and enjoyed many privileges and Kumudvati's son Atithi respected her like his own mother.
Mata Sita
And of course who can forget Mata Sita who is epitome of strength and purity. She was foster daughter of Janaka and daughter in law of Dashrath and she never ever wavered from her loyalty towards her husband and always preferred her self respect and her own agency more than anyone else. She was an extremely morally strong lady, when Shri Ram acted to forsake her just so that she would be provoked to give test of purity, she took it to prove her love and also her the purity of her character. Later Shri Ram said that all this was done so that no one would question her, he himself had full faith in her and Ravana couldn't dare to touch her because she was protected by her own moral power. She was an extremely mentally strong lady. Yes, she did cry, she did feel fear but she surpassed that and always stood up for what's right.
The Queens like Tara, Mandodari, Sulakshana (Sulochana), Kunti, Gandhari were also very strong and wise ladies.
The Princesses of Ramayana and Mahabharata era were given proper education and they were taught many skills as Kaikeyi was a warrior, Draupadi was an administrator and she also looked after finance, Mandodari was Chief Queen of Ravana and she had her own contributions , Kumudvati was a homemaker but she enjoyed being so and raised Atithi so well that he was called jewel of Nagas and Raghuvansh.