Ok I’m not going to start this by slating you or your BF OP.
Advice: she’s 2 or 3, so a toddler and the best way to go about this is not to force yourself upon her. I understand this is hard, especially when your already in a routine with your son, and so I’m sure it just seems both fair and convenient to just include her in that, but don’t. Instead you offer things to her, DS and I are going to brush our teeth now, do you want to come and brush yours too? If she’s come along and joins in great, but if she doesn’t don’t be offended. You give her the option and if she doesn’t want to join in, her dad can see to her after all that’s his job. Same goes if your doing something fun with DS, for e.g let’s say you’ve got some crafts out let her clearly see what you are doing, I’m sure it will peak her interest and when she comes closer welcome her warmly and again ask if she would like to join in. Basically you just need to let her come to you, allow her a little bit of control to decide if she wants to join in rather than just automatically including her by default. I think if you do this you’ll get a much more positive response. It will take a bit of time, but if you tread carefully and slowly and allow her time to adjust to the situation, I’m sure she will warm to you.
As she is non verbal, she may well struggle expressing herself at your home which in turn is going to lead to some frustration and challenging behaviour. Mothers often understand their non verbal children very well, almost like a code only they can interpret and so communicating her wants/needs may be very much easier at home. I don’t know if her dad has his own way of understanding her but I’m guessing from what you’ve written that he doesn’t, or just isn’t as fluid at it as her mum is. I don’t know if your BF and his ex are amicable, but if there are this is a conversation they need to be having. It would be useful to know certain things for instance that DSD tends to get angry/frustrated if she’s tired/hungry, or that when she rubs her feet together she needs a nap etc. Maybe it has just been assumed that dad knows these things or that he would work them out for himself, or maybe he already knows but has omitted to share these with you. So these are some things to consider going forward.
For what it’s worth I do agree with other posters in that your BF needs to take a much more active and hands on parenting role with his DD. I understand how easily it can be for you to fall into the default carer especially when your already doing this for your son but that itself doesn’t negate his need to parent his own child. Lastly make sure he spends time alone with his DD without you and DS around. At DD’s age an hour or two alone is sufficient, he could take her to the park or do an activity with her while you and DS do something else as you need quality one on one time with you Ds also.
Blending families is hard, and it’s a long ever changing road, rest assured there will always be challenges.