Lyssa Chapman, who starred on Dog's reality TV show, tells TMZ ... she would like to send her apologies to Dylan and the trans community as a whole, and her heart breaks over Dog's hateful comments.

The apology comes on the heels of an interview Dog gave Tuesday, where he launched a homophobic tirade and took shots at Dylan and Bud Light.

In reference to Dylan, Dog said ... "People playing church all led to Bud Light. Is that right? Get that punk down. Rebuke Satan out of him and just give him a couple black eyes. That's exactly and I mean that. If I ever see him, I'm dropping him."

Lyssa says Dog's comments are not in line with her father's character (though he more than doubled-down) ... she feels that's not who Dog is and she says she's trying to find out why he said such nasty things.

Dog's daughter tells us they spoke on the phone after the interview, and she says it was mostly just them yelling and talking over each other ... the conversation, she says, was far from productive.

Lyssa says Dog's comments do not reflect the morals he taught her growing up ... and she loves him, but worries he's watching too much cable news.

Dog's other daughter, Bonnie Chapman, also released a statement aimed at her father, saying, "Jesus loves everyone and would strongly denounce this non-accepting rhetoric. It is utterly repulsive to to advocate violence against our transgender community, and it is equally repulsive to invoke Jesus' name in vain to support such views.