Mi dispiace. Credevo che tu volessi solo parlarmi con me (1) a causa di mio padre (2).

Notes

(1) "*Parlarmi con me" is ungrammatical, because it contains two overlapping constructions. You can say 'parlarmi' (whose non clitic variant is "parlare a me"), which comes from "parlare a qualcuno", or "parlare con me", which comes from "parlare con qualcuno". Since their meanings are a bit different, to choose the correct one for your text, it would be useful to know what exactly you want to say: did the speaking person expect to essentially listen and the other person to speak (informing him, reproaching him, asking a favour of him…) or was he referring to a discussion? In the first case I would use 'parlarmi', while "parlare con me" would better describe the second scenario.

(2) I'm not sure about the meaning of "solo parlarmi / parlare con me a causa di mio padre": could you, please, say it in English? Is it "I thought that the only thing you wanted to do was to talk to me because of my father" or "I thought that the only thing you wanted to do was to talk to me about my father" or again "I thought that you wanted to talk to me just because of / about my father"?

Please check my sentence

good :)