Like I said, the children need your undivided attention for a while. You have only been separated for three months...for the kids, that's still the "traumna" stage. How long it will take will depend on the children's adjustment....PARTICULARLY the 3 year old.
However, I am not suggesting that you have to continue to visit at mom's house. I am suggesting that you insist on your visitation rights, but let mom know that your girlfriend won't be part of things until the children have had more time to adjust to the divorce. Let her know that you realize that your kids need to have your undivided attention during your time. I would give it at least 3 months with the children getting your sole attention during your time, and then maybe gradually have your girlfriend around a bit for at least another 3 months, but not overnight.
Your children are more important than anything else....and they are suffering more from this divorce than you and your wife are. Particularly the three year old. Even if she isn't showing it...she really is suffering. The one year old won't remember a time when you and mom were together, but the three year old will for a long time.
My ex and I split up when our daughter was three. Even a year later she was constantly asking me to buy presents for daddy so he would want to come home. No matter how much I reassured her that daddy and mommy both loved her, and that sometimes daddy's and mommy's didn't live in the same house...she still suffered for a long time.
Luckily I didn't have to worry about my ex having her around his girlfriend (the one he left me for...sigh...) because he read an article by a psychologist that talked about the importance of focusing his attention soley on his child for a while. Therefore he refused to even consider introducing her to his new love interest for a VERY long time.
Sure, you believe that your girlfriend will just be another person to give them love....and you aren't really wrong. However, you didn't make it with their mother, and that is traumatic for them. If you make her a major part of their lives, and then you don't make it with her, then they will suffer traumna again.
However, again, right now they need your undivided attention.