I think that they do love you.
I also think that they are being typical teenagers. This doesn’t excuse their behaviour but that is probably the main reason for it.
If I were you I would treat them like children. That is how they are behaving.
They make the comments because they are struggling with hormones and confusion about their own place in the world and it makes them feel better to put you down.
They see you react to them, so don’t react. Be as cool as a cucumber.
I would refuse to respond to every negative remark. Just meet them with total silence, don’t even make eye contact. If they ask you why you are not responding say something along the lines of ‘I don’t respond to disrespect, when you are ready to treat me with respect I will be here for you’. Don’t say it in a preachy way, don’t be ‘holier than thou’ just be matter of fact and cool.
I would also limit my contact with them as much as is physically possible. Don’t give them your attention until they treat you better.
I hope this situation improves.