There are many places to visit in Gujarat. Sharing few of them here: 1. Dwarka
2. Gir Forest
3. Champaner - Pavagadh 4. Gandhinagar
5. Saputara
6. Diu
7. Dholaveera
8. Bhuj
9. Mandvi (Kutch) 10. Sardar Sarovar Dam - Statue of Unity There are many more places but keeping it short.
The plan seems OK. But with kids, I would advise you to add Switzerland or Germany. There are many things for kids there. Avoid Europe from Dec to March. It's very cold and snow. For details on Europe trip planning you may check out my posts.
Taj mahal is built in a large area I dont think there will be any python or snakes inside taj mahal, warning you about the parks by side of it is dangerous. If it is in news and anyone has complained, security would have definately taken precautions
Yes you can visit Sakleshpura at any time of the year. Most of the places in Karnataka have been receiving above avg/high rainfall this year so be cautious before you travel.