Bickering kids!

Hi imperfect parents, was after some advice please ... I have a 7 year old son with ADHD and HF ASD. It's been him and I since he was nearly 2, however he does have a good relationship with his Dad and sees him fairly regularly. My son is medicated for his ADHD and has therapy for his ASD. I am in a relationship with a lovely man (together over a year) and he has two kids, a 9 and 6 year old. We stay at his place weekly and are working on getting to know each other and the kids seem to have accepted our relationship really well, including adjusting to both my partner and myself (couldn't ask for better, to be honest). However the two younger kids (7 & 6, both boys) just bicker and argue constantly! My partner and I are at our wit's ends, we just feel like we are breaking up arguments and fights all weekend. There are times that they get along well and can be really kind to each other but then next minute the boys are arguing again!! I'm probably not used to it as I've only ever had one child, but surely it's not meant to be like this! It's putting my partner and I off wanting to move in together. The youngest boy seems to antagonise the oldest (at times - both boys antagonise each other) and the oldest can have trouble at times controlling his temper and takes the youngest's comments to heart (he's very sensitive). The youngest's behaviour is generally better due to him not having special needs so he tends to tell the older one off a lot. His father does pull him up for it and I do the same when my son is in the wrong. When my son is not around my partner's kids are great - the oldest (girl) is no trouble whatsoever and I love hanging out with her. And my son is certainly no angel either - it's a challenge. So I'm not blaming any particular child, just wanting some advice/tips please.
Thanks!