Suggested tire pressure for an "overloaded" bike I've got very old (10+ years) Author Mystic bike. It has 26" x 1,95" tires with suggested pressure set to 2,9-4,5 bar. Currently I have inflated them to 3,4 bar. I'm around 120 kgs and riding on such tires brings no problems for me.

I'd like to start riding with my older daughter in bicycle child seat. She is less than 20 kgs (near border weight for that child seat).

Answers to this Duru Can Celasun's question assured me, that in general my bike should handle our together weight of 140-150 kg without serious problems. Though, we may already talk about overloaded bike with such weight of user.

Here, I'd like to ask, what would be perfect tire pressure for both my lonely rides (120-125 kg) and for together trips (140-150 kg)?
Generally, the tire pressure range marked on the tire is somewhat loose - the marketing department wants a big range since it will sell better, the legal department wants a small range so liability is lower and the engineers have something probably bigger than whats marked on the tire as safe. Your tire pressure should be high enough that you don't get pinch flats but not give a harsh ride. The links in the recommendations show roughly what tire deflection should look like. Note that lower pressures are generally more comfortable. 

150 kg on a bike is a lot - most companies will mark this as higher than the max weight for their non-touring/cargo bike models (so you're on your own legally). That being said, I have carried a lot more on bikes marked significantly less, you're on your own with that. 

As for tire pressures which are best, you have to find this out on your own - its dependent on terrain you're riding over, your daughter's stomach, etc (and the best tire pressure (which is largely subjective, hence why I'm voting to close the question) will depend on the load on the bike so if you wanted one pressure, you'd have to trade off between the no daughter and daughter rides). 

There are some recommendation charts and manufacturer recommendations to start with - tweak your tire pressures to your liking.