Are there scholarships for a physics PhD in Germany that don't consider income?
Disclaimer: this is just my experience with scholarships in Germany, there exist for sure other scholarships with possibly varying conditions. I'm chemist, but I think that's close enough to physics in terms of which scholarships you can apply for.

So, here are my 2ct:

I had a PhD student scholarship (Telekom Stiftung) where the conditions worked actually the other way round compared to what you describe: the scholarship was a fixed amount, but there was a condition that you work full time at the PhD project and do not have any (or only very minor) side jobs.  

Before that scholarship I also had a part-time contract with university. I then got leave for the scholarship from my university position and meanwhile university paid someone else with the TA money. This way, both my institute and I profited from the scholarship: I had the scholarship (including also travel budget etc) and my institute could pay another (part time) position. 


"Scholarships for traveling expenses" are usually called "travel grant", so you may want to search under this term. 
Conferences may have travel grants for students, you'll have to check them one by one
If you are member of DPG, ask them for travel grants to their conferences/workshops/...
If you institute participates in a EU COST action, you may be able to apply for a short term scientific mission (STSM) visiting another institute of the same action. 




I just saw that the Studienstiftung allows up to 25% part time jobs in research for their PhD scholarships.

Note that both my Telekom scholarship and the Studienstiftung scholarship limit the amount of time you put into other jobs, not the income generated (and the Telekom never asked about other sources of income). 



Getting slightly off-topic:


More recently, I've seen PhD projects that looked quite like scholarships, but the money was given to university who employs the students rather than giving the money directly to the students as a scholarship.
When calculating the financial aspects of scholarship vs. university part-time job, do not forget that these are very different wrt. to social insurance (and taxation)!
Scholarships that consisted of a fixed part (for books etc.) plus a variable part depending on (parent) income I've met only for Bachelor/Master/undergrad studies. The variable part was set up along the lines of Bafög. AFAIK that is quite common for the undergrad scholarships.
Which PhD scholarship are you referring to? (Just curiosity)