I was in a similar situation when I first met my dh, his previous relationship had been with a woman in her forties (he was in his early twenties). They had been split for several months when I met him, I actually knew his ex before meeting dh, she worked at somewhere I was receiving treatment for my health. She had always been absolutely lovely with me until my dh started taking me to my appointments. She became strange, cold, bitchy and they would whisper outside in private while I was in being treated. I could see them from the treatment room.
I actually spoke to dh about it several times and he explained it as having had treatment there himself previously. Eventually, after another bitchy appointment, I confronted my dh and was told that they had been in a relationship and then explained their relationship in far too much detail. I was jealous, but more so because it had been kept from me and that every time I had been in getting my treatment, they had been having private conversations about me (our relationship, whether he had told me about anything etc)!
My dh would also text this woman frequently, it pissed me off and truth be known he was a complete ass hole about it all. Looking back, I think she felt he was too young and was embarrassed to be seen out and about with him. This had initially hurt him so he used me to rub under her nose, seeing as I was very young, naive, pretty and inexperienced. This obviously worked, as she suddenly had an older man she was seeing with her a lot. It was honestly like two five year olds trying to make each other jealous! I got fed up with it all and told him to either start behaving like a grown up and leave his ex where she belongs in the past, or I was finished with him. Thankfully my treatment was over, he realised that actually he was falling for me and felt way more for me than he had for his ex and didn't want to risk losing me. He was just bloody young and stupid, she wasn't much better either!
I am not sure if this is the case, but there could be an aspect of your db enjoying showing you off, in order to make his ex jealous. My dh admits it now, 16 years later and profusely apologises when it is brought up. He denied this was the case at the time but it definitely was even if at a subconscious level. Let's be honest, there is absolutely no need for you to have to keep seeing his Mums friend! You can organise to take his Mum for lunch/ dinner, there is no need to invite the friend!
In your place, I would tell your db that you are not prepared to put up with his ex's childish jealousy and nasty behaviour, tell him that he could easily stop this by asking to spend time with just his Mum. If he refuses to, tell him that he must get off on making his ex jealous then and that you are not prepared to stay around to watch it! This should have been nipped in the bud at the very first meeting! If you love this man, then you want to have a good relationship with your potential MIL, the last thing you need is a jealous best friend whispering nasty comments about you into your db's Mums ear!
I do get what you mean about the icky aspect, I was very grossed out at the time, but it was definitely my green-eyed monster and insecurity, thinking that I wouldn't be experienced enough for him as his ex-was so much older! It was awful, too picking up on the sexual chemistry that was still there between them! I honestly don't think I could have continued in the relationship if this behaviour had continued! Thankfully it didn't, my dh couldn't even remember his ex's name recently when we were talking! To be fair it was a lifetime ago!