Hi Baz
Sorry mate I have only just seen your question!
Here are a couple of thoughts.
The most important thing is that you and their mum approach this together. You guys HAVE to be on the same page and they need to see mum give you permission and freedom to discipline them, parent them and have control.
Have you both sat down and discussed a way forward? The reward chart is a good idea but if it was up and running before you arrived maybe it might be worth coming up with a new one/idea/concept. for example if they currently have a star chart type thing that gives them a reward if they reach 10 stars in 1 week, move to something else like a penny system. But the approach is that when you talk to them do it together one evening before bedtime. It needs to start with mum say “ WE have been talking and WE have decidedâ€
The penny system could work in that they start with 10 pennies (they are only 3 and 5 yrs old after all!) and lose a penny for bad behaviour and are rewarded a penny for good behaviour. At the end of the week they count their penny’s and go to the sweet shop with you. I would also suggest that for the first month you have the task of rewarding good behaviour whilst mum seeks to pick up on bad behaviour for the main part. This will break any perspective in their minds around you playing second fiddle to mum.
If you don't like the penny idea try thinking of some others.
Also try getting regular “Family Time†and calling it that. Mum esp needs to be very verbal about FAMILY and including you in that time. Do they call you dad or is it to early for that? Can i ask a very forward question! How long have you been living together, how used to havig you around are they?
I would suggest you need to be very proactive in having fun ideas through which to engage with them. Take them on 1-2-1 times where it's just you and the 3 yr old then you and then you and the 5year old. Take them to the park and play, take them to a coffee shop for a muffin. take them swimming or to the cinema. (divide and conquer my friend! 😉 )
Every now and again bring them home a small gift like a packet of sweets or cheap toy or magazine. Saying things like I saw this and thought of you reinforces that you consider them to be a part of your life.
It take on average 66 days to learn a new routine or mind set so give them time to see what's going on through the above ideas.
One top of all this remember that the 5 year old is going through some big life changes with schooling that opens his/her world up to the outside world. It can be quite intense for them and they may not know how to deal with it. If they have up till then had lots of close time with mum they might simply be missing her and play up more when she is not around because of that. The 3 year old will simply follow suit.
check out these
child dev articles for 3 and 5 year olds
Also what is their love language? how do they give and show love? find this out and then demonstrate your love through that. ie time, gift, touch (hugs, tickles etc) words of affirmation.....
Hope this helps bud. Let us know how things go.