First off, Grens are not useless (and anyone saying they are need to l2p and gtfo of this thread).
My usual build order vs Brits / Americans is either:
MG, Sniper, Gren, Gren, Sniper, Gren
MG, Gren, Sniper, Gren, Gren
Snipers do require lots of micro and looking after but they bleed both those factions very hard. Imo USF doesn't really have any decent sniper counters. Always screen your sniper with Grens and keep enough muni for a faust or two, even if it means delaying LMG upgrades. Placing early tellers as well and keeping your sniper near these will easily deal with an m20. Most players will get tunnel vision when they see a sniper and try to kill it, so its easy to take advantage of this.
Regarding Bren carriers, without a flamer they are not very dangerous. If you see one its worth teching fairly fast to T2 and getting a 222 down (will lock down Wasp very easy and provide decent sight for snipers). If they Brit player builds his own sniper, just wait for a counter snipe opportunity. Always have the sniper in cover and screen with Grens. Let his sniper try to shoot your Grens and catch him this way. Its a game of patience but will pay off in the end.
Otherwise, rifle grenades are pretty potent, especially vs people who don't have great micro. Sometimes a preemptive rifle grenade will work wonders. If you a squad approaching cover, fire it so that it lands just as they get there. Always keep units together, never sent anything alone (unless a pio squad to cap, make sure to retreat them fast if anything more than a RE appears). Try to stick with your team mate early on as well (map depending). Makes it very hard for "blobs" of infantry to get past several mg's with infantry screening.
If you are having problems with them smoking mg's, a PzGren with a cheeky nade in the smoke works wonders as they advance through it.
Teching after T2 can go one of 2 ways depending on how you are doing for map control and resources.
Tech T3 and get Stugs / PzIV's. Despite what some people say. PzIV's are still pretty potent vs infantry and can win 1v1 vs Shermans. Stugs are great vs Medium tanks but do suffer vs Jacksons. Ostwind imo is only really needed if they are going super heavy on infantry and lacking on armour.
Tech T4 and get Panthers / Panzerwerfers. Panzwerfers will wipe out infantry blobs very easily and they are pretty effective right now. Panthers are pretty decent vs all USF armour. Best thing with a Panther is to keep it at max range and reverse if something tries to push on you. You will bounce quite a decent % of shots this way but can still penetrate their armour. You want to make the allied players have to invest and commit lots of forces to kill a Panther.
In terms of doctrines there are a few choices and depends on what your partner is doing.
Lightning war is probably my favourite. JU-87 is very powerful and against as well as infantry. If you can manage to drop it on a Major / Ambulance, it will do heavy damage. Tigers are still decent vs USF thanks to their range buff. Will do decent damage against Rifles and are pretty durable - be wary using them when Jacksons are around though. I really like G43's as it gives a more constant damage output and makes gren much better and Mid / Close range as well as better dps while moving. Depends what the USF player is doing regarding weapon upgrades. Relief infantry can be pretty handy just to use as meat shields or extra capping squads.
Jager Armour is a strong 2v2 commander on fairly open / long maps. As long as its supported well with Grens / Paks, its pretty difficult for USF to take down.
CAS can work well but it depends on the map and the micro of the opponent.
If you are still having issues, I would suggest uploading some replays and ask for help as well as watching your own as well, regardless of whether you win or lose. Failing that, play USF for awhile and see what gives you problems. Regardless of how "easy" or "OP" USF is, you will get beaten sooner or later. Seeing how people beat you will give you ideas of how you can win.
FWIW, I'm pretty much the only one with high level 2v2 Automatch ranking / experience here (and most people are hiding their player card).
Any questions fire away