"I shouldn’t have had a daughter like you." or "I shouldn't have a daughter like you."
Hi Tiger,
It is possible for you to use the present perfect (i.e. have had) as you speak. In this case, you are expressing regret at something that started in the past and is still taking effect at the present (you should have started regretting having a daughter in the past).
On the other hand, if you are expressing your regret at a present situation, the present simple tense (i.e. have) does the job.
So yes, the present perfect tense can be used to express a current situation which is linked to a past origin. It really depends on the time frame you wish to specify.
I hope this helps.