Advice or opinions

My daughter and I live in Missouri while her dad lives in Texas & his parents live in Louisiana. Her dad is not actively involved in my child’s life , he barely tries to make an effort to see her he’ll go months without seeing her , i always have to literally force him to make time for her , and when he does I always have to travel to him. For some reason he will not travel to come see her he’s probably came to Missouri 3 times to see her , all the other times I’ve had to go out there. His parents don’t make any effort to come see her either , they never call to check on her , and this is there only grandchild. I always have to call them or video chat them in order for them to see her , So really his parents and him or complete strangers to my daughter . Well all year they’ve requested can she come out there for Christmas i told them yes BUT I will be out there with her . Her dad and I or not together and for the past few months he’s been asking can he get her for a month , me personally am not comfortable with my one year old daughter going away for a month not even a week , so we’ve been arguing back and forth about that. But we came to an agreement that I will be out there with her for Christmas, cause I know my child and she will not be comfortable being out there alone without me . Right now she doesn’t see him as a father nor does she see them as her grandparents, I’ve never kept my baby away from them It’s like they don’t care to try to make any effort to being in her life , I’m literally tired of having to call them first or randomly send pics just so they can see how big she’s getting. It’s like they all are getting comfortable with me making the first move. Anyone have any advice or opinions on this situation? Am I wrong for not letting her go out there by herself for Christmas? Should I stop making the first move all the time ? Should I stop all calls and sending pics and let them call first for a change? Like I don’t know what to do I want to teach my daughter that it’s not her responsibility to reach out to grown people in order to have a relationship with them.