I agree that it is apprpriate for you to speak to your mother, show her the texts, and explain how uncomfortable they made you feel, and that they went against what you had said to her.
However, looking at it slightly from the other side:
You told your mother that you and your siblings didn't want to meet her partner. He (or your mom, or both) may have felt that a text was a first step towards that. A text is not a meeting. I think this comes over from bob's text - he seems to be trying (clumsily) to open a door to future meetings.
I agree that the comment about your mom not being happy can be read as a dig at your dad but I wonder if this is to some extent down to the lack of tone and context in a text. I wonder whether your mom had had a conversation with Bob where she'd made some comment such as "They don't want to meet you - I think they blame me for the break up and disapprove of the fact I've met someone new" 'Don't blame your mom' doesn't automatically mean' blame your dad' - it may equally mean - 'don't blame anyone - these things happen' (and of course his understanding of what happened and why the marriage ended will be based on what your Mom has told him
I think the whole text can be read as a well meant but clumsy attempt by Bob to take on board your reluctance to meet and to try to address the (perceived) reasons.
obviously that doesn't in any way mean that your reaction to it is not perfectly valid, but I think there is a strong possibility that this is well meaning but clumsy, rather than deliberately ignoring your boundaries. For that reason, when you do speak to yyou Mom, I would be very clea in focusing on hopw the messages made you feel;
e.g. "I felt that this was putting pressure on me"
" I was surprised as when I told you we were not ready to meet Bob, I also meant I didn't want to speak to him or hear from him, so when he texted me I felt as if he was ignoring that boundary"
"I felt that his comment about not blaming you came over as a dig at dad, and I feel uncomfortable with that"
"Him telling me not to blame you made me feel I was expected to pick sides. I don't want to apportion blame between you and dad"
The daughters text specifically says she was asked to contact you so I would give her a pass- she's got the message at least third hand (you spoke to you mom, your mom spoke to Bob, Bob spoke to his daughter) She may well have been told nothing more than "It's be nice for you and my girlfriends children to get to know each other - here's her number, an you give her a text or call?. She's trying to be friendly (and of course, she may be over-compensating for any doubts she has about her dad being in a new relationship, too) I would be inclined to reply with a brief text saying something like "thanks for the offer. Our parent's separation is very recent so we're not ready to start getting to know Bob or his family yet." it doesn't encourage any future communication but equally it doesn't lose the door on it, in the event that Bob and your mom do stay together and you do get to know them in the future.
