I hate confrontation and I can see how in your situation I would want to be avoidant to keep the peace, and get out of the situation without fully explaining why.
When asked to BBQ, dinner etc, have you explained that the dog is the reason you refuse?
If you always give an excuse that doesn't mention the real issue - she will never know.
Ie if you always make an excuse of a previous commitment, it's too late, your too tired etc, from her point of view you are always rejecting her and she (being thick skinned and blind about her dog) probably doesn't have a clue why you never come over and will indulge in feeling hurt and affronted.
It is blindingly obvious to you (and anyone sane) that you don't want your baby around a dog known to bite, but she obviously can't see this.
A frank conversation needs to be had. Worded in "I" terms : "I am worried about the dog being around the baby."
If you start verbally attacking her with "YOU" terms, telling her what she has to do - she will automatically go on the defence : "You need to shut your dog away etc"
I am not naïve enough to think you saying "I am worried about the dog being near the baby as we know he has bitten before and I don't feel able to bring our baby to your house when the dog is running free " will have her saying "of course dear, we must put the dog out of the way. "
But if you present your feelings to her (collectively your husband saying "WE are concerned about..." ) as much as she may not like them - she will know them. These are your feelings and concerns and you need to express them as such.
Present your fears and concerns to her and then let her decide what she will do. Again, not in a confrontational way - but in an adult way.
If she is all huffy and offended - that is HER choice. You didn't do this to her - SHE chose to react like this.
Keep the moral upper ground by being purely logical and factual as to how you see the situation and that you are keeping your child safe. Don't insult her, don't raise your voice to her. Politely ask her to hear you out and just set out the problem.
She will be shocked beyond belief that you have 'dared' to speak to her like this - but if you do it calmly and rationally, she has to then decide her response.
I think honesty and openness will be unusual for her, but I would make it your policy. Just be polite and clear.
If he can't say it he can write it to her - Shit Sandwich approach. (Good, Bad, Good)
Bread - I love you mum and hope you understand that I need to talk about something concerning me. I appreciate how much you love DOG, I love my family very much too.
Shit - The dog situation (in WE feel.. terms)
Bread - I love you and respect you and hope you understand I never want to upset you, but I need to be honest about how I feel and I look forward to working out how we move forward. We want you in our lives and this is a barrier that we really want to overcome.
Good luck!