Want to get an idea if my 2 year old is developmentally delayed?

i'm stepmom to a 2 year old, we only get her 120 days out the year and its split up to about one month every 3rd month, she is very spoiled for one, but is starting to learn she can't be like that with us, but she doesn't seem to understand things you are saying, just looks at you puzzled when given a simple task and has the same words a 9 month old has, (mama dada baba) but she doesn't know who is mama and dada, she calls everyone that and she babbles like a 9 month old, has 5 somewhat coherent words tops. everything else seems on track as far as growth, play, eating with fork and spoon, yet still on baby sippy cups because her mom is too lazy to break her and she starts potty training with us but reverts back every time she goes to her mom. is there an internet test i could take before i pay a bunch of money for a professional? i'm not sure if it's a delay or the way she is treated, her mom dumps her at her grandmas all the time who apparently treats her like an infant, she was still having her drink from a bottle at 15 months! and another thing that may just be spoiled-ness but she refuses to walk most of the time, wants to be carried on your hip everywhere or she throws a huge tantrum on the floor convulsing and everything.