You would be required to come to Chandigarh (A lot of cabs, autos are available at station). You would get buses and cabs from Chandigarh.
No idea about the cost, but it would take around 10 hours to reach Manali from Chandigarh!!
Kalka - Rupanagar (earlier Ropar) - Bilaspur - Mandi - Kullu - Manali. There two ways to do Kalka - Rupanagar (one through Baddi and other through Chandigarh), the latter is very good roads and given the early hours no rush at all (Baddi route not sure about road quality). It will take you around 7-8 hours of driving plus stops given the early hour you are starting.
Shimla route will be longer and more hill drive so not sure it makes sense from a shortest route perspective.
Cost is approx. Rs. 10-14 per km - but you need to pay both ways (it is 325 km from Kalka). If you can manage a good deal, may not have to pay two ways. There should be plenty of buses from Chd.
Dilip - assume you have some work in Ludhiana so need to be there (otherwise how can you reach Ludhiana without crossing Chandigarh? and if you do, why reach Ludhiana and start immediately). I have the following comments:
1. Manali needs minimum 3 days (else too rushed), skip Shimla and do Manali.
2. You are covering two different regions in one trip but not doing either fully. Suggest that you combine Manali with something closer like: Manali - Kullu - Tirthan Valley - Shimla OR Manali - Shimla - Kinnaur. It will save you a lot of travel time and you will see places which are much better than Nainital.
Alternatively you could also drop Manali-Shimla completely and do Kumaon trip instead, i.e. Nainital, Kasauni, Mukteshwar, Munsiyari.
With small kids, try not to do too much road travel and spend more time at the destination. You can look up Manali, Kinnaur and Kumaon threads here for details of various places to visit there.