would you say that a bitch becomes more sure of herself and more stronger in her temperment after she has had her first season?

Generally yes, because she's starting to mature and not be a submissive puppy.

so im right in thinking that it during this time that bitches that ussualy got on, would start to show problems if there is going to be any?

In my experience there might be minor disagreements more to do with how the hormones make them feel.  Matters of status are more likely to come up between puberty in my breed at 3 to four years of age.

Of course in a more domineering individual/breed puberty may be enough to trigger vying for position.  My own bitches have been very easy going and with good age gaps the natural order of things happens smoothly.

My oldest bitch abdicated/was deposed from top spot by her Granddaughter when they were 11 and 5 years respectively and just after the younger one had reared her second litter.

I have found having a litter markedly elevates a bitches sense of importance, and do have to watch they do not get above themselves (if lower ranking) so as not to upset the status quo.